OHIO University Mechanical Engineering Concept Report

Greenhouse Tarp Covering System

Team Tarp-e-diem

Tyler Smith Chad Stroud Ronald Bolin

Michael Bruce Robert Rushton

11/17/2011

Abstract The content of this report shows the initial concept generated to provide a covering system that meets the customer’s specifications set in the project proposal. The report discusses how the concept was generated along with other possible solutions. The different concepts were vented using multiple decision matrixes as well as analytical analysis to determine the cost and feasibility of each design. The final concept is a three wire system that crosses the width of the greenhouse that will support the cover five feet off of the ground. The wire system will be constrained with concrete in the ground and the tarp will move by a series of looped ropes powered by a single manual crank.

1.0 Concept Generation 1.1 Problem Statement for Concept Generation

The overall development of the project is aimed to produce a system that will allow a farmer to produce crops in the Midwest 365 days a year. The climactic changes that occur in winter do not allow for crop sustainability due to the subfreezing temperatures, however through capturing geothermal energy, organic crops have been grown year-round for the past five years at Green Edge Gardens.

The method currently being used is placing two tarps over the plants during the winter. Covering the produce with the tarps should be improved to decrease man hours, improve efficiency, and increase heat retention. The process needs to be considerably shortened to save labor hours. Currently, it takes two employees roughly four minutes in the morning and evening to cover and uncover each of the eight greenhouses (64minutes total/day—two people). Team Tarpe-diem’s goal is to create a system that takes about one minute to cover and one minute to uncover each greenhouse (16 minutes total/day—one person). This will be faster than the previous method, reducing man hours, while requiring only one person to operate. One of the customer’s main necessities is to be able to operate the system using only one person, due to the difficulties associated with finding workers to be present every day. The efficiency will be improved by the ability to replicate the tarp placement. The current tarp placement may be skewed by a multitude of factors, which could be corrected by having a tarp guiding system. The ability to have a guiding system for the tarp should also allow for better storage and condensation drainage. Heat is lost from multiple heat transfer methods which will need to be explored in order to maximize heat retention. The customer believes the majority of the heat transfer is due to convection of the geothermal energy away from the tarped surface area.

Concept generation was initialized by identifying these problems and researching other solutions. This was done by examining existing patents and shopping for systems that already solve these problems. This was completed by studying existing designs that cover and uncover large areas. When this was done it was determined that no existing system meets the requirements of customer. All of the current systems either use fossil fuels or wood to heat the greenhouse or have large volumes of water used to absorb heat during the day and then release it during the night. Due to the cold days in the Midwest gathering heat during the day was not possible and using fossil fuels or wood was not practical because of operating costs. Systems using geothermal heat by pumping water underground and then to the greenhouse were determined to have too large of an installation cost. The only practical solution is to use some form of covers to prevent the ground from cooling down during the winter.

1.2 Patent Search

Keywords: Crank, Rail, Tarp, Cover, Plants, Covering System, tarpaulin, retractable, collapsible, removable, roll-up, cable anchor, cable support, ski lift, greenhouse

Relevant patents:

1. US Patent Number: 8047600

Tarp enclosure system

A retractable tarpaulin cover system includes a tarp cover, plural spaced substantially U-shaped bows supporting and connected to the tarp cover, movable carriages operably connected to lower ends.

http://www.freepatentsonline.com/8047600.html

Thoughts: This system is used for a truck and their width is only about 9’ so a pole over the top is not hard. Our greenhouse width is 30’ and they do not manufacture poles that large for an

affordable price. The tracking system used here will be way more than our $500 budget. The accordion folding function may be helpful to our design thoughts though.

2. US Patent Number: 7980619 Flexible Tarp Bow with Spring Member

An improved tarpaulin bow for use primarily on a vehicle trailer in which the bow is selectively movable in a downward direction.

http://www.freepatentsonline.com/6612638.html

Thoughts: This hanging rail system could be very useful in our project as we will need some way to use gravity to keep our wheels in line if we decide to change our design to a rigid rail system.

3. US Patent Number: 7905051

Abstract: The present invention relates to a system for promoting the growth of plants under less than optimal climatic and lighting conditions, the system comprising a device which

contributes to the formation of an enclosed space over the plants, and at least one source of light. A special characteristic of the invention is that the device which contributes to the formation of an enclosed space over the plants consists of a flexible tarp which comprises integrated lighting sources, the flexible tarp being kept up at an optional height over the plants by means of excess pressure built up under the tarp by means of an excess pressure system.

http://www.patentgenius.com/patent/7905051.html

Thoughts: This method is good for sports fields that must only cover grass, but our crops will grow to about 30” and this will not apply because we do not want to support the tarp on the produce. Also, the second method for this system’s support is a pressure system, which is not

applicable because we do not want to use any power for our system. The patent speaks of using grow lights, where we are using only ambient sunlight.

4. US Pat. App 10255904 - Filed Sep 25, 2002 A tarp or other fabric to be held on the roof would be placed in position. A removable fastener for holding a material.

http://www.google.com/patents/about?id=xfGRAAAAEBAJ

Thoughts: This could function as a tarp attachment method, but it seems that this would be a more costly approach than metal clamping.

5. US Patent Number: 1985509

Cable Anchor

http://www.google.com/patents?id=ood5AAAAEBAJ&printsec=frontcover&dq=cable+anchor&hl=en&ei=zi68TvGeDaf30gHJgK3fCQ&sa=X&oi=book_result&ct=result&resnum=3&ved=0CDUQ6AEwAg

Thoughts: This would be a good method for our cable support which will minimize friction on our cable. The patent has expired so it is owned by the public (1934)

6. US Patent Number: 5240303

http://www.google.com/patents?id=-yIpAAAAEBAJ&pg=PA18&dq=tarp+cable&hl=en&ei=aC-8TveXEqXm0QGx0ajeCQ&sa=X&oi=book_result&ct=result&resnum=2&ved=0CDMQ6AEwAQ#v=onepage&q=tarp%20cable&f=false

Thoughts: This system is very similar to the system we are creating; however, there are some differences; this system is automated, much smaller, and features a chain and sprocket mechanism.

7. US Patent Number: 2582201

Ski Lift

http://www.google.com/patents?id=PkphAAAAEBAJ&pg=PA1&dq=ski+lift&source=gbs_selected_pages&cad=2#v=onepage&q&f=false

Thoughts: The cable mechanism could offer some thoughts on how we would be able to provide incremental supports to our long cable runs to prevent excess deflection.

8. US Patent Number: 5241782

Wire-form crop cover support

http://www.google.com/patents?id=K10bAAAAEBAJ&pg=PA1&dq=Patent+5241782&hl=en&ei=bzi8TtXsN7SPsAKf84nQCA&sa=X&oi=book_result&ct=result&resnum=1&ved=0CDAQ6AEwAA#v=onepage&q=Patent%205241782&f=false

Thoughts: This freestanding system is good for support separate from the plant; however the system would still require two people to pull the tarp over because there is no tracking system. Our customer desires to operate the system with one person only.

9. US Patent Number: 2007/0051054

Retractable Greenhouse

http://www.google.com/patents?id=2dKjAAAAEBAJ&pg=PA10&dq=crop+cover+retractable&hl=en&ei=ATu8TprxMsqAsgL90NWcCA&sa=X&oi=book_result&ct=result&resnum=3&sqi=2&ved=0CDUQ6AEwAg#v=onepage&q&f=false

Thoughts: This is very similar to what we need to be doing with both the folding of the cover and the cable supports. This method does not use a large amount of concrete and cable tension requirements should be explored further.

10. US Patent Number: 4296568

Agricultural Crop Cover

http://www.google.com/patents?id=WdIBAAAAEBAJ&pg=PA1&dq=crop+cover+retractable&hl=en&ei=ATu8TprxMsqAsgL90NWcCA&sa=X&oi=book_result&ct=result&resnum=1&sqi=2&ved=0CC8Q6AEwAA#v=onepage&q=crop%20cover%20retractable&f=false

Thoughts: This seems to be a similar cover which is used to protect agricultural crops. This system seems to be more complex than our design entails, but employs fixed supports and a plastic cover. The cost of this system would exceed our budget set by Green Edge Gardens.

1.3 Concept Generation

Once the research phase was completed it became apparent that there was no system that could be modified to meet the customer’s needs. The research did help the group by showing many different ways in which the tarp could be supported, moved, aligned, and stored. The next logical step would therefore be to takes these subsystems and find ways to incorporate them into a design that would serve the customer’s needs.

To generate the subsystems the 5-3-5 method was used. This involves five people generating three ideas in five minutes and then each person in the group silently spends five minutes reviewing and making suggestions to improve the design. This method worked remarkably well for the group, so it was decided to perform this again at the next meeting. Each person would bring the three concepts with one covering movement, support, and alignment. After this iteration the discussion broke into more of how each subsystem would interact with other subsystems. It was therefore determined that complete systems needed to be discussed.

In this iteration every group member was required to bring a design for a complete system to the meeting. At the start of the meeting each group member presented the design with no one else in the group talking. Then each design was passed around the group were everyone got a chance to offer suggestion to improve it. Once that was finished the group began to disuse each design and the merits of each. It also became clear that two members had very similar designs and two others also had very similar designs. One design was different from the rest. It was decided that these designs should be merged together, which would leave three designs left.

The final iteration of concept generation was refining these three designs with the hope that all three could provide a potential solution. This was done by drawing each design on a white board and preforming the 5 hats approach. Each group member was assigned a certain area of focus when analyzing the design. The goal of this was to try to find and correct the problems with each of the individual designs before entering concept selection phase. Once this was done three polished designs were created and ready for selection.

2.0 Concept Screening and Evaluation

2.1 Concept Screening

After the concept generation process the ideas were analyzed in different aspects to determine what was feasible and what needed to be redesigned. The concepts were presented to Green Edge Gardens for feedback and improvements. There were three concepts that were considered during this process. It is necessary for the concepts to be run by one person in a timely manner. Also if plant health or tarp life can be improved the concept will be better.

Concept one includes a rail system that travels the length of the greenhouse with a 30 foot long 2 inch pipe to roll the tarp. One employee would roll the tarp the length of the greenhouse to cover and uncover the crops while the rails guided the roller and distributed the tarp evenly. This concept is an improvement in storage of the tarp and it decreases wear on the tarp. With a rolling system the tarp won’t get as dirty and it makes for easy storage during the summer. The roller would be supported by a rail system that travels the length of the greenhouse. This rail system would need to be able to support a 25 -150lb tarp depending if it were dry or wet, and a 30 foot pipe. These rails would need supports dug into the ground and require a large amount of construction inside the greenhouse. After talking with Green Edge Gardens there would be a problem with price and construction because the crops would be affected by the in ground supports and there is very little room for the construction since crops are still grown year round. In addition, the concept needs improvement because it needs to be removed during the summer so the larger crops are able to grow without interference. The 30 foot pole also causes a problem because there would be a large deflection over the length it runs.

Concept two consists of two cables that will be connected to concrete dead weights buried in the ground. The cables will be used with a pulley system to cover and uncover the crops. The tarp will be supported by the cables that will run above and it will never touch the plants or any supports. The tarp will be stored in an accordion style fashion on the north end of the greenhouse, where less light is blocked, so it will never come in contact with the ground. This concept should improve the tarps life because the tarp will not come in contact with any wire or the ground. A support pole will also be used in this design and needs to be buried in the ground with concrete like the dead weights. The dead weights and support poles will be located outside of the greenhouse. One concern that has been brought up about this system is the wire going through the side of the greenhouse. Tests need to be done to determine if a seal in the side of the greenhouse will affect the overall temperature and plant health.

Concept three consists of a roller, crank, pulley and rail system to cover and uncover the plants. The tarps are to be rolled up using the roller and deployed using a pulley system. The rails would be attached to the sides of the greenhouse so the tarp is guided out and in to the roller correctly. Since the rails will only support the end of the tarp and not the roller the greenhouse will be able to support the rails. Guide wires will be used to keep the tarp off the plants. Tarp

longevity is a factor in the designs and it needs to be better or at least the same as the current system that the tarps last three years. Dragging the tarps over guide wires everyday could increase wear to the tarps and decrease their overall life. Although the tarp will be in more contact with the wires it will have less contact with the ground so tarp life may not be affected. Tests will need to be carried out to see what the effect the wires and the ground have on the tarp.

2.2 Data and Calculations for Feasibility and Effectiveness Analysis

This section examines the different solutions and determines if there are any problems with the designs from a structural side. It will also be used to determine the parameters for the designs that can only be found with calculation. An example of this would be determining the size of the dead weight supports for concept two. These types of parameters will greatly affect the group’s decision, because they can show if an idea is possible and or practical.

Concept One:

Concept one is a rail system that travels the length of the greenhouse with a mobile roller that will travel along the rail and roll up the tarp. In this system the roller is thirty feet long and is made of two inch pipe. It will have to support its own weight and the weight of the covers, 150 lbs. This makes the total weight 250 lbs. and if the weight is assumed to be evenly distributed the roller will have a distributed load of about 0.70 lbs/in, see Figure 1. The major concern for this system is the defection in the roller which would cause binding on the wheels.

Figure 1: Free Body Diagram of Moving Roller

Solving this type of problem will be done using equations found in the equations attachment. With the given values there will be a 5.9 inch defection in the roller, which would bind the wheels. To correct for this the person rolling the tarp would have to lift with a force of about 100 lbs. this is a statically indeterminate problem, to remove most of the defection. This is an excessive force for an individual therefore without modification this system is not practical.

Concept Two:

For concept three the two cables will be connected to dead weights made of concrete buried in the ground, see Figure 2. The wire running from the support pole to the dead weight must be at least seven feet because the power puller that will add the tension to the wire is six feet and there needs to be some room to connect it to the wire. With those two lengths the rest of the angles in the system can be found using trigonometry. These angles will be used in the free body diagram, Figure 3, to calculate the forces on the dead weight.

Figure 2: Drawing of Wire System Connection to the Anchor Point

Figure 3: Free Body Diagram of Dead Weight

The first thing that needs to be determined to find the size of the dead weight needed is the force that will be applied to the support wire. It has a maximum design load of 2000 lbs. and therefore a force of 1500 lbs. will be applied to have a marginal factor of safety. Using the known geometry that force will broken into a vertical component of 857 lbs. and a horizontal component of 1232 lbs. The weight of the concrete and the friction the ground provides will hold the vertical force component. With the friction unknown, a safety factor of 1.2 seems reasonable because the weight of the concrete will hold the dead weight in place regardless of the friction.

This solution will require the concrete to have of weight of 1028 lbs. Since concrete has a density of 133 lbs/ft^3 (ref 1) the dimensions of the hole need to be found so it will have a large enough area to meet the desired weight. A hole with a diameter of two feet and a depth of two and a half feet has a volume of 7.85 ft^3. This multiplied by the density of concrete gives a weight of 1040 lbs. which meets the requirement for the vertical force.

The support wire also exerts a horizontal force that will have to be restrained by the bearing load of the dirt. The bearing load of dirt in southeast Ohio is 2000 lbs/ft^3 (ref 2). Only half of the surface area of the dead weight will apply the force to the dirt therefore the surface area of the dead weight must be found which equals 7.85 ft^2. This means that the support can withstand a horizontal force of 15700 lbs. or in this case have a factor of safety of 12.72.

The forces on the vertical support pole are similar to those of the dead weight, see Figure 4. For the support pole the horizontal component is 1232 lbs. and the vertical component is 857 lbs. The horizontal component will be transmitted along the wire and to the pole; vegetable oil will be used to remove friction. The vertical force needs to be supported by the dirt that can hold 2000 lbs/ft^2. To increase the area of the pole concrete will be used. The depth of the concrete has to be at least 30 inches because that is the code due to the frost line. The diameter should be at least one foot to allow a shovel to enter. This would have an area of 0.785 ft^2 and would be able to support a load of 1570 lbs. The total volume would be 1.96 ft^3 and would therefore have a weight of 261 lbs. This would make the total normal force to be 1118 lbs. and there would be a safety factor of 1.40 without taking friction into account.

Figure 4: Free Body Diagram of Support Pole

The final step is to find how much material is required to make all of the concrete. There are four dead weights and four support poles with a total volume of 39.24 ft^3 of concrete. There are several ingredients that go into making concrete: cement sand course aggregate, and water. The ratios are 1 part cement, 2.5 parts sand, 2.5 parts aggregate and ½ parts water. That is a total volume of 6.5 ft^3 if one part is one cubic foot, that is how they are sold, per cubic foot. This 6.5 will shrink by 2/3 so the total volume is 4.3 ft^3 per batch. If ten batches are made that will provide 43 ft^3, a little bit extra for waste and measurement errors.

From the previous calculation it shows that there is about 1200 lbs. of tension on the support wire were it supports the tarps. A way to analyze this problem is that the tension on the line will counteract the downward force of the weight of the tarp and wire, see Figure 5. This would be because as the wire goes down the large force of the tension will now have a vertical and horizontal component. This could be analyzed by seeing how much force would be required to cause a one foot defection downward. This would make a triangle, as shown in Figure 6, with an angle of 1.27 degrees. When a force triangle is applied with this angle and 1200 lbs. the horizontal component caused a vertical force of only 26.7 lbs. There are actually two force triangles, one force each side, therefore that force would be doubled to 53.4 lbs. This defection also increases the length of wire and therefore the tension on the wire.

Figure 5: Free Body Diagram of Support Wire

Figure 6: Triangle Drawings

Using the same triangles in Figure 5 the new length can be found, 90.02222 feet or 1080.2667 inches. The original length in inches is 1080. Using the strain equation, Equation 1, the strain can be found to be 2.4688 E-4. Then the stress / strain equation, Equation 2, with a modulus of elasticity of steel being 3.0 E7 lbs/in^2, (ref 3) the added stress to the wire is 7.4065 kips. When equation 3 is applied the added force can be found to be 363.6 lbs. This can then be added to the original force to get a total force of 1563.6 lbs. This total force gives a vertical reaction force when the wire is defected one foot of 70 lbs.

The wire is known to be able to support 70 lbs. with a one foot deflection but not the total weight that the wire will have to support. The known wet weight of the of the tarp is 150 lbs. so when the tarp is half way retracted a weight of 75 lbs. will be split between the two wires. The remaining 75 lbs. of tarp will be still weighting on part of the line therefore it can be conservatively assumed that it will add 10 lbs. The cable will weigh 60 lbs. over the entire length so that will account 20 lbs. in the center. The total force will be near 70 lbs. so the one foot defection is an accurate estimate.

Note: All of this information was entered into a Catenary Curve calculator, (ref 3) and the total displacement was 0.84416 feet. This is probably the most accurate solution because the actual wire will act as a Catenary curve and not a triangle. The triangle equation are a good approximation and much easier to understand.

This means that the four foot support pole length is to short. With a one foot defection in the wire, ½ foot defection in the tarp, one foot fold when contracting, and 2.5 foot high plants the tarp will contact the plants. To prevent this, the pole height needs to be increased to five feet.

This can be done without changing everything but by just increase the length of the support wire from the pole to the dead weight. This will keep the angles the same and therefore all of the forces.

Loading the wire will increase the wire length therefore this increased length need to found to ensure that it does not exceed the maximum allowed by the wire tightening device, 24 inches. This can be done by using the stress / strain relationship found in equations 1, 2, and 3. That value is 0.88 inches but it does not take constructional stretch into account. Constructional stretch is removing the spacing in the wire fibers. This will be 0.5% of the total length of wire or 5.4 inches. This makes the total change in length 6.28 inches which is within speciation.

There is a large force placed down on the support poles which could cause them to buckle. This force is off the centroid of the column therefore this column should be treated as a eccentric column. With all of the complexity of this problem the specification and list of equation will be provided but not the exact method. The equations are 4-8 and the lists of variables are found in Table 1.

Table 1: List of Variables for Support Pole Bucking

Description Variable Value

Outside diameter of pole Do 2.375 inches

Inside diameter of pole Di 2.083 inches

Pole length L 60 inches

Force applied to pole P 857 lbs.

Yield strength in compression Syc 26 kips

Distance from centroid to outer edge c 1.1875 inches

Distance from centroid to point of force e 1.1875 inches

Modulus of elasticity E 30 Mpsi

The bucking stress is 2733 which is nowhere near the yield stress of the steel, 26 kips; therefore the pole will not fail.

As shown with these analyses there is nothing technically impossible with this design. While preforming this analysis it was found that this design will cost much more then original estimated cost, mostly due to the increase in wire strength and the size of wire required. The only true unknown left is how much the tarp will sag when wet. It was assumed that it would only drop six inches but this will have to be examined during the lab testing phase if this design is chosen. If the tarp does lower more than expected then the pole height could be raised to compensate for that.

Concept Two Modification: In concept two the tarp travel the length of the greenhouse, 90 feet, but a logical modification to this design would be to have the tarp travel the width of the greenhouse, 30 feet. This would increase the span that the tarp would go unsupported, so an extra wire was added to help prevent the tarp sagging. The system is shown in Figure 6. For this system there will be three wires that support the weight of the tarp, and this makes the system statically indeterminate. There are three unknowns: R1, R2, and R3, and only two equations to find them, the sum of forces and the sum of moments.

Figure 7: Free Body Diagram of Modified Concept Two

The total weight of the tarp is known to be 150 lbs. when wet. When the tarp is half retracted it will cause the maximum defection. This would cause 75 lbs. in the center and 75 lbs. spread over the other half of the line. For simplicity a total value of 100 lbs. can be assumed. The weight of the wire can be found by neglecting the weight of the coating and assuming that the wire is solid. With the density of steel being 0.283 lbs/in^3 and at a length of 30 feet with a

diameter of ¼ inch, the weight is 20 lbs. That is for each wire so the extra force of 5 lbs. should be added to the force at the center.

There is a conservative but incorrect way to solve this statically indeterminate problem, bringing it in half. By doing this R2 assumes half of the total load and R1 and R3 each take a ¼ of the weight. This would make a force on the center of R2 to be 55 lbs. with R1 and R3 being 30 lbs. each. If R2 meets the defection requirements then so will R1 and R3.

Concept two modifications are very similar to Concept two. The methods for solving all of the unknowns are the same and the support pole height and dead weight placement are also the same. It would therefore be easiest to see the difference between the two designs by showing a table of values for each system, Table 2.

Table 2: List of Concept two

Variable Concept two, 90 foot travel Concept two, 30 foot travel

Force on wire (lbs.) 1200 600

Defection in wire (inches) 12 6

Defection in tarp (inches) 6 (assumption) 12 (assumption)

Total defection (inches) 18 18

Force on support pole / Vertical force on dead weight (lbs.)

857 580

Diameter of dead weight (inches) 24 20

Diameter of support hole (inches) 12 10

Volume of dead weight (ft^3) 7.85 5.26

Volume of support hole (ft^3) 2.36 1.36

Total volume of concrete needed (ft^3)

43 43

As Table 2 show there is not much difference between the two systems from a feasibility standpoint. The similarity in the forces and distance also leads to the cost being almost identical, see cost section. The differentiating these concepts will have to be done with other means than calculations.

Concept Three: Concept three is a system that has pulley connected to the top of the greenhouse on the far end and is connected to a hand powered crank on the ground. The tarp travels the long way across the greenhouse. On the near end is a roller that stores and retracts the tarp. This roller has a 27 foot long section that is unsupported and will have to hold the weight of the tarp, see Figure 8. The question is if the shaft can support the required weight over the required distance.

Figure 8: Free Body Diagram of Hand Powered, Fixed Roller

The first step is to find the total weight that the shaft will have to support; it is assumed that the weight will be evenly disturbed over the shaft. The shaft has an outside diameter of 2.375 inches and an inside diameter of 2.083 inches. It is made of lower grade steel; this will not affect the displacement but will affect the breaking stress. With those dimensions the weight of the pole is 93.75 lbs., therefore with a wet tarp the total force of 243.75 lbs. Using the equations in the equation attachment the maximum moment is 9872 lbs.-in and has a maximum displacement of -5.64 inches in the center.

This large of a displacement would cause huge issues when trying to operate. With a two inch outside diameter and a goal of one minute cycle time this would require a three revolution per second cycle rate. This large displacement with a fast cycle time would cause massive instability and potential failure, the moment alone causes stresses is near the yield point. If the shaft diameter was increased to 5 inches this would help with the defection, -1.30 inches, but that would have to custom order for that length and would be very expensive. Without a support underneath the shaft this system is not possible.

Concept Three Modification:

In concept three the problem was a large defection in the support shaft and in the modification a spring/roller system was installed help alleviate this, see Figure 9. There will still be some defection in the center because the weight of the shaft changes as the tarp is removed. By setting the force of the spring to 80 lbs. this will cause a one inch defection upwards when the tarp is removed and 0.8 inch defection when the tarp is installed. There will still be some defection in the two unsupported sections of the shaft.

Figure 9: Free Body Diagram of Hand Powered, Fixed, Supported Roller

When the defection in the two short sections are calculated using equation appendix one the defection is 0.31 inch. This will be an independent defection that is caused by the spring. These defection values are low enough so that they would not greatly affect the shaft while rotating. This modification removes the problem will issue three and therefore makes it possible.

System Cost: One of the most important variables when selecting a design is cost. If the system cost too much then the customer will not implement the design to the rest of his greenhouses and then the problem was not truly solved. The cost that was estimated that would lead to implementation was 500 dollars. This was based on three years of labor savings. If the design increases plant growth and decrease plant loses due to mold that would increase the value of the system and therefore how much the customer would be willing to pay for it. Currently all of the concepts are over the 500 dollar limit as show in Tables 3-6.

Table 3: Concept One Cost Table

Material Company Spec Cost per Unit

Number of Units Needed

Actual Costs

Rails Lowes 25 16 400 Pipe (2 inch Rigid Conduit) Lowes 45 3 135 Bearings/wheels Lowes 31 1 31

Clips 2 4 8 Coupling Lowes 3.5 2 7 Concrete Lowes 4 11 44 3/16 Nylon Rope McMaster 61 lbs. 10.29 3 31 Steel metal Lowes 20 1 20

Total Cost 676

Table 4: Concept Two Cost Table

Material Company Spec Cost per Unit

Number of Units Needed

Actual Costs

5/16 Vinyl Coated Steel Cable

McMaster 7000 lbs. 1.66 200 332

Maasdam CAL-1 1 Ton Power Puller

Amazon 2000 lbs. 23 2 46

Metal Pulley Lowes 50 lbs. 4 5 20 Stainless Steel Wire Rope Clip

Lowes 3.5 8 28

3/16 Nylon Rope McMaster 61 lbs. 10.29 6 62 2 inch Rigid Conduit Lowes 45 3 135 Mobile Home Anchors Lowes 20 4 80 Cement Lowes 9.34 10 94 Sand Lowes 3 32 96 3/4 Coarse aggregate Lowes 3.25 32 104 Plastic Pipe 0.602 ID McMaster 300 psi 28.36 1 29 Clips 20 Hand crank 20

Total Cost 1066

Table 5: Concept Two Modification Cost Table

Material Company Spec Cost per Unit

Number of Units Needed

Actual Costs

Wire McMaster 3700 lbs. 1.17 150 176 Metal pulley Lowes 50 lbs. 4 5 20 Stainless Steel Wire Rope Clip

Lowes 3.5 8 28

3/16 Nylon Rope McMaster 61 lbs. 10.29 6 62 2 inch Rigid Conduit Lowes 45 5 225 Mobile Home Anchors Lowes 20 6 120 Cement Lowes 9.34 10 94 Sand Lowes 3 32 96 3/4 Coarse aggregate Lowes 3.25 32 104

Plastic Pipe 0.602 ID McMaster 300 psi 28.36 1 29 Clips 20 Hand crank 20 Maasdam CAL-1 1 Ton Power Puller

Amazon 2000 lbs. 23 3 69

Total Cost 1063

Table 6: Concept Three Modification Cost Table

Material Company Spec Cost per Unit

Number of Units Needed

Actual Costs

Pipe (2 inch Rigid Conduit) Lowes 45 3 135 1 1/2 inch Rigid Conduit Lowes 35 6 210 3/16 Nylon Rope McMaster 61 lbs. 10.29 4 42 Concrete per hole Lowes 4 26 104

Bearings (stainless steel) McMaster 1000 lbs.

83.07 2 167

Sheet Metal Lowes 1 15 15 Metal Rings McMaster 2 5 10 Pipe for handle Lowes 15 1 15 Hand crank Manufacture 50 1 50 Metal Pulley McMaster 250 lbs. 5.85 1 6 Metal Wheel McMaster 12 2 24 Spring McMaster 18 2 36

Total Cost 814 All of these are estimates and were done without extreme price comparison. It could be assumed that by refining the designs and better shopping practices that the costs could be lowered by about 10 to 15 percent. Another factor is that with any project there will be unexpected costs, try to do a pluming job and only go to the store once. This will most likely remove any cost saving that could be found.

Heat Transfer / Tarp Analysis: In all of the conceptual design listed above there is an assumption that the same tarps will be used as are currently being used, one plastic tarp and one cloth tarp. This two tarp system was devolved because when a single plastic tarp was placed on the plants then it would cause frost damage to the plants were it made contact. It could therefore be assumed that if the plastic tarp did not touch the plants then the cloth tarp would not be needed. To determine if the cloth tarp is need there need to be an understanding of the tarps currently keeps the plants warm.

In southeast Ohio the average ground temperature six feet below the surface is 55 degrees and this heat source combined with the greenhouse and tarps do not allow the temperature to

ever get below 40 deg. Heat is lost from the ground to the air and to the surrounding ground. The surrounding ground heat losses will not change with any of the designs so it will not be analyzed. The heat loses to the air are impeded by a series of barriers and this heat has to pass though each one of them to escape. This is similar to an electrical circuit with the heat being current, and the temperature difference acting as voltage. This makes each barrier a like a resistor and the total system can be shown as a thermal circuit, see Figure 10.

Figure 10: Simplified Greenhouse Thermal Circuit

For this thermal circuit four of the terms are air. For the three terms that are inside of the greenhouse the way air moves heat is by using natural circulation; heat rises and cold sinks. There are a series of equations that are used to determine how much this happens and in one of those equations is a temperature terms. This makes sense because the greater the temperature difference the greater the driving forces would be. This creates a problem because to find the total heat transfer rate the individual temperature must be found. To find the individual temperature the total heat transfer rate must be known. If there were one term that were needed then it could be found by guessing some values and then solving over until it were correct. With three terms there would be possibility for this to be useful. It is therefore assumed that the temperature difference between each layer is eight degrees Celsius. A table of all other known values is listed in Table 7.

Table 7: Heat Transfer Data

Variable Value

Outside air temperature -20.55 C Plant temperature 4.47 C Outside area velocity 5 m/s Current area of cover 295 m^2 Concept two area of cover 362 m^2 Greenhouse Area 788 m^2 Actual cloth thickness 0.003 m Modified cloth thickness 0.0075 m Plastic tarp thickness 0.001 m Greenhouse wall thickness 0.002 m Thermal conductivity plastic 0.25 W/M*k

Thermal conductivity cotton (cloth cover) 0.06 W/M*k

In Table 7 there is a term listed modified cloth thickness and it has a large impact on the analysis. In the greenhouse the cloth tarp is placed over the plants and then the plastic tarp is placed over that. This means that there will be sections of the plastic tarp that do not make contact with the cloth tarp. These sections will have a much greater resistance to heat transfer than the sections that are in direct contact. To correct for this the cloth tarp will be assumed to have a greater thickness and to be in direct contact.

The best way to try to understand this problem is by comparing the resistance of the cloth and plastic system to that of just a plastic system. In the plastic system using the values listed and assumed the total resistance is 0.67 W/(m^2*k) and in the cloth and plastic system it is 0.80 W/(m^2*k). That is about a 17% increase when using the cloth.

There are also different areas which are directly proportional to heat loss. In concept two the area was increased by 19% so this should also increase the loss of heat. This means that by changing the design to concept two with only a plastic sheet it will increase the rate of heat transfer by about 36%. This is very large increase but it still might work. The reason is it is not known how much heat the ground releases. If the current system is barely putting out enough heat now then this would be a very bad idea, but if the has a large reserve of heat and can take the extra load then this would have huge plant health implication. More research will have to be performed and it may only be known by preforming real world testing. Another solution that needs to be looked into is installing a frost barrier along the perimeter of the greenhouse. A frost barrier will preserve more heat under the greenhouse causing the temperature inside to stay warmer longer. Frost barriers are usually made of Styrofoam and a plastic cover. They would need to be dug into the ground around the greenhouse. This solution will need to be looked at further to determine if it is needed and if it is cost effective. If the frost barrier does work it could eliminate the need for a two tarp system.

2.3 Concept Development, Scoring, and Selection

This section discusses how the final project idea was chosen. It shows how individual ideas were critiqued and rated along the process to selecting a final idea. Initially there were five ideas presented by the group. The fourth and fifth ideas were similar enough to be combined into one of three main concepts stated in section 2.2 above.

Once the three main concept ideas were formed each group member presented their concept on a whiteboard. The concepts were then intensely critiqued for their pros and cons. All three concepts were done in a similar fashion. After the ideas were critiqued, a decision matrix was used to rate each concept based on four different categories. The decision matrix is located in Figure 10 below.

Figure 10: Decision Matrix

The method of finding the values for Figure 10 are presented in the following paragraphs. Weight

Plant health was given the highest weight because if the plants do not survive the winter with this system than the whole project is a failure. Single person operation was given the next highest value because one of the client’s needs is for the system to be run using one staff member. This will decrease the hassle of finding another worker and will decrease the money spent on wages each year. Construction is more important than maintenance because if the client cannot build the system himself, the project is also a failure.

Reference A

The current system cannot be operated by a single person, it is hard to operate, and cannot be finished in under a minute. This gave it the lowest possible rating. It received less than perfect marks because the tarp currently lies on the ground in between plants and when not in use, which shortens the life of the tarp. Also there is some constant maintenance with the wire bracing the tarp lays atop. There is virtually no construction needed so it receives high marks. Currently there is approximately a 10% loss of plants due to various plant health problems like frost and mold.

Concept 1

This can be operated by a single person but probably will not meet the one minute time. It has a relatively high strength requirement and is a concern with the safety of operation. There will be almost no maintenance with concept 1. The system is not very adaptable and is specific to the greenhouse. However it does use commonly used parts. Regarding plant health, this system projects decent sun exposure and frost protection but below average moisture drainage.

Concept 2

This system has a low strength requirement, small safety risk, and is likely to achieve the one minute goal. The attaching clips could damage the tarp over time as well as some maintenance with the retracting system. It is easily the hardest to construct but is very adaptable and uses commonly used parts. It has good sun exposure and frost protection as well as good moisture drainage due to the way the system is stored in an accordion fashion.

Concept 3

Concept 3 has a medium strength requirement, with an achievable one minute goal. It also has an average safety concern. There is some concern with tarp being pulled over the wire supports that are used to prevent the tarp from touching the plants. This could cause some maintenance issues in terms of tarp life. As far as construction, concept 3 is above average on all aspects but not perfect. Regarding plant health, this system also projects decent sun exposure and frost protection but below average moisture drainage.

The four main ways the concept was judged were single person operation (one minute goal, strength requirement, and safety), maintenance (tarp longevity, maintenance), construction (ease, adaptability, commonly used parts), and plant health (sun exposure, frost protection, moisture drainage). These were the four main areas of concern with the overall project no matter the design. The reference A is the current concept that is being used by the client. The final totals are highly sensitive to a small number change. Each concept is within two points of each other. A small change in the effectiveness of the plant health for instance could put each concept even with each other. That being said, Figure 10 shows that concept 2 is the best current idea with concept 3 being the next best.

There were still a few flaws with each concept design. For concept 1, a large amount of deflection occurred at the center of the 30 ft. long tarp cylinder. The deflection was high enough to warrant significant concern. In concept 2, there was concern with the wire cable, sagging and contacting the plants over the long distance. In concept 3, again there was deflection in the center of the 30 ft. cylinder.

From this point, concept 2 and 3 were modified to better handle these challenges. Concept 2 rotated 90 degrees so that the tarp was only being pulled 30 feet instead of 90 along with the installation of a third wire. This greatly reduced the tension needed to hold the wire taught and also the amount of sag in the wire that would occur. Concept 3 saw the addition of a spring to the center of the 30 ft. to help support the load. This modification can be seen in Figure 11.

Figure 11: Concept Modification Matrix

Ratings

Concept 2 scored higher on the single person operation because of the probability of meeting the time requirement with a small force. Concept 2 also pushed ahead in the

maintenance category because concept 3 requires a large cylinder to hold the tarp which would need some upkeep as well as the braking system. Concept 3 beats 2 in the construction category because concept 2 requires putting in a large amount of concrete in order to hold the tension required to keep the wire taught. Concept 2 edges out concept 3 in plant health because there is no way to eliminate the moisture when the tarp is rolled up.

From this point on concept 1 was basically scraped due to the challenge of reducing the deflection in the tarp cylinder. This could not be solved easily to the group’s knowledge. The next way that concept 3 was broken down was by power source. This matrix is shown in Figure 12 below.

Figure 12: Manual verse Electric Matrix

Figure 12 shows that a manual power source edges out the electric power source by a slim margin.

Ratings

The electric method scores slightly higher than the manual for safety because the manual has moving parts that must be hand operated creating the possibility of harm to oneself. Cycle time for the electric method is also higher because a motor can be started with a button and does not rely on human power to operate. Construction will be much longer for the electric system which decreases its rating significantly. Electric motors also cost a lot of money which is an important part of what the client is requesting. The electric motor is a little more likely to require maintenance because it has moving parts that are controlled by a computer. The manual method requires a lot more energy to operate thus the lower value for ease of operation.

Another matrix was used to further differentiate which of concept 2 and 3 was the better idea. Figure 13 below shows an adverse consequences matrix for both a cable and rail system.

Figure 13: Consequence Matrix for Cable verse Rail Systems

.

Figure 13 shows that a cable system is slightly more preferable than a rail system in this case.

So far every matrix that has been used has shown that concept 2, the cable system, is slightly better overall than both concept 1 and 3. This does not mean that either concept 1 or 3 cannot be built or will not satisfy the conditions of the client. It merely shows that concept 2 will more likely succeed at meeting these conditions.

Looking further into concept 2, a matrix was developed to see which method of retracting the tarp was better. The original method retracted the tarp the entire 90 ft. of the greenhouse and the modified version retracted the tarp only 30 ft. Figure 14 shows the comparison of the two.

Figure 14: Concept 2 Design Matrix: 90 ft. verse 30ft.

Ratings

The 30 ft. method has a higher safety rating because it requires less tension in each rope to hold the tarp up. With less tension there is less chance of being hurt. The 30 ft. method has a higher construction time however because more concrete gussets are needed. There will be 6 instead of 4 corresponding to the additional wire added. Since the 90 ft. method has a length of wire unsupported for 90 feet there will be almost double the wire sag. The reverse can be said for tarp sag. For the 30 ft. method, there is a 45 ft. section that the tarp must be pulled taught over compared to only a 30 ft. section for the 90 ft. method.

The final total points to a slight lead by the 30 ft. method of concept 2. This is the concept that made its way to the end of the design process. It has undergone a few changes and additions thanks to the help from the decision matrices.

3.0 Final Design Concept After proceeding through the concept generation, evaluation, and development team

Tarpe-diem was able to develop a speculative design. The main components of the final design are grouped into a few system subcategories: rail system, cable support system, tarp system, and crank system.

The rail system’s material will be 3/16” braided steel cables with a vinyl coating. There will be three 30’cables with one cable placed between the centers of the 96’ sides of the greenhouse and each of the other two cables will be 45’ from the center cable. These rails will function as the guiding structure for the tarp. Steel cable has a tendency to deflect over large distances; however, with adequate tension (600 lbs.) this will not be an issue. Using the simplifying assumptions of linear deflection and triangular segments, the deflection is -6 inches at the center of the cable with a distributed load (weight of tarp) of ~150 lbs. (further detail in Section 2.2). In order to provide this tension, an external cable support system will be required.

The cable support system includes both the support poles and the concrete anchors. The support pole material will be 2” rigid conduit. There will be two support poles for each cable, each of which will extend 5’ from the ground’s surface. In order to support the 600 lbs horizontal component of tension the conduit must both be sunk into 30” deep of concrete and the cable will extend to an additional dead weight concrete support (see Figure 3 in Section 2.2). The support cable will attach to the concrete via a mobile home anchor eyebolt 5’ from the support pole. Roughly, 2.86 tons of concrete will be required to create the required dead weight supports. The concrete dead weights counteract both the vertical and horizontal components of force created by the cable tension. The taught cable allows for easy expansion and retraction of the tarp.

The tarp system’s material will have two material layers one is cloth and the other is Typar® (further testing will be used to see if the cloth layer is required). This industrial plastic offers a large strength component while remaining transparent. The durability of the tarp will allow for adequate tension from the supports. The supports are a folded Typar® section attached to a 1” length of ½” diameter polyvinyl chloride (PVC). The PVC segment travels around the vinyl coated steel cables. The spacing of these supports will be 2’ in order to both add sufficient tarp support and allow for tarp folding hanging only 1’ when retracted. The tarp folding when retracted will save space, keep a majority of the tarp off the ground, and promote moisture drainage. When the tarp is fully extended it will cover all of the crops and extend to the ground, which will allow for most of the geothermal heat to be captured during cold winter nights. When the tarp is fully retracted, it must be stored in close proximity to the north wall. The material contact between vinyl and PVC greatly reduces friction, which inherently decreases human power required for tarp extension/retraction through cranking.

The crank system provides the motion of the tarp. The design utilizes a hand crank, pulleys, and ropes. The design will have two positions, fully extended and fully retracted. There will be four ropes each having their own corresponding pulleys. The ropes will be attached as seen in attached sketches. The pulleys direct the ropes to the correct tarp attachment locations. The pulleys also offer a method to extend and retract from switching the direction of manual cranking. The crank will be attached to a 4-rope collection roller to keep each of the ropes separated, which will prevent entangling.

For further information on calculations and decision-making strategies, see Sections 1 and 2. The preliminary construction method of the final design will cost $500-$1000 when procuring all parts from commercial home improvement stores.

Appendix

References 1. http://www.cement.org/tech/faq_cement.asp

2. http://www.concretenetwork.com/concrete/footing_fundamentals/why_soils_matter.htm

3. http://www.spaceagecontrol.com/calccabl.htm?F=1200&a=90&q=1&g=32.18503937&Submit+Button=Calculate

4. http://www.stren-flex.com/wire-rope-technical-info.aspx

5. Norton, Robert. Machine Design: An Integrated Approach. Pearson, New Jersey. 2010.

Equations

Equation 1: Strain equation. 𝜀 is strain, l is final length, lo is initial length

ε = 𝑙−𝑙𝑜𝑙𝑜

Equation 2: Stress / Strain equation. E is the modulus of elasticity, σ is stress

E = 𝜎𝜀

Equation 3: Stress equation. P is the applied load, Ao is the original area

σ = 𝑃𝐴𝑜

Equation 4: Area of the support pole

A = 𝜋(𝐷𝑜2− 𝐷𝑖2)4

Equation 5: Second moment of area

I = 𝜋(𝐷𝑜4− 𝐷𝑖4)64

Equation 6: Radius of gyration

k = √ 𝐼𝐴

Equation 7: Slenderness ratio

Sr = 𝐿𝑒𝑓𝑓𝑘

Equation 8: Buckling Stress

σc = 𝑃𝐴 ( 1 + ( 𝑒∗𝑐

𝑘2 ) * sec( 𝑙𝑒𝑓𝑓

𝑘 * √ ( 𝑃

𝐴∗4∗𝐸 ) ) )

Equation Attachment One:

Sketches:

Checklists:

Checklist Item Y N Notes for this Decision: The issue requiring a decision has been stated clearly and is understood by all members of the team.

x Matrices have been created to quantitatively make decisions.

The deadline for making the decision is set, based on its priority and relation to the overall project schedule.

x We are to come up with alternative designs over winter break, and the commence of winter quarter is the deadline.

The decision maker(s) who has final authority for making the decision has been identified by team consensus.

x The team decides on important decisions by consensus only.

The impact of the decision on the overall project has been determined, and the appropriate time and resources for making the decision have been scheduled.

x Impact is established by the pair wise matrix weighting.

The reversibility of the decision has been assessed, and if the decision is reversible the latest reversal date and process for reviewing the decision prior to that date have been scheduled.

x Deadline for concept generation is the beginning of winter quarter.

The impact of the decision on safety (including any aspect from manufacturing through customer use) has been assessed and safety critical items have completed or been scheduled for a Design for Safety review prior to decision approval.

x A factor of safety is required by law on cable tension, which is the most dangerous design feature. We have run hand calculations on this.

The data or information required to make a good decision has been identified, gathered and reviewed, and all other people or things that could influence the decision have been consulted.

x Basic building materials have been used. Experts have been used when assessing calculations (Dr. Kremer, Dr. Cotton, Dr. Womeldorf, TJ Cyders, etc.)

The process for making the decision has been identified by team consensus and appropriate tools and documentation have been used. Diversity of team member perspectives and cognitive styles was used to ensure that multiple alternatives and adverse consequences (risks and implications) were considered (as applicable), and sufficient intellectual debate / conflict occurred concerning the leading options. The final decision does not appear to be merely the ‘least common denominator’ of the options.

x There have been multiple meetings, discussions, and arguments involving all of our design concepts. A consensus has been achieved on our final proposed design.

The cognitive biases that impact decisions were discussed and addressed, including confirmation bias and the tendency to accept opinions as facts.

x We had a meeting where everyone started to agree because we were all tired; therefore, we ended the meeting early.

The need for external review and approval of the decision has been determined, and that external review has been completed or scheduled within the overall project schedule.

x Our mentor has approved both our project proposal and concept design.

The results of the decision have been reviewed by the team, and lessons learned from that review (what actually happened as a result of the decision versus what they expected to happen) are used to build team skills for decision making.

x The team has learned about the most efficient approaches for decision making and task delegation.

Checklist Item Y N Notes for this Decision: The Conceptual Design decisions have been reduced to the appropriate scope for the most effective decision process.

X Various matrixes have been used to aid in the decision of the final concept. This helps in considering every possible problem or issue that could arise in the concepts.

All applicable items in the SrD Decision Checklist have been followed for the significant CD-related decisions.

X Yes they are explained in the prior checklist.

All relevant questions about assumptions, feasibility, risks or other aspects of the conceptual design alternatives have been addressed.

X Numerous calculations have been made to ensure the feasibility of each concept. We have narrowed it down to two main concepts and there are pros and cons for each.

All alternative solutions that have been used in other industries or fields that merit comparative evaluation in the concept selection process have been included.

X An extensive benchmarking section was done in our previous paper and the systems that were researched have certain aspects that have been transferred to our designs.

Patent research has been executed and evaluated, and any unique and potentially valuable technology in the design concepts has been considered for invention disclosure and patent application.

X Different patents have been researched and applied to our designs. There wasn’t any direct involvement currently in our designs but we may incorporate some in the future.

The maintenance and repairability of the final concepts was included in the system-level conceptual design and the selection of the final concept.

X In our matrixes maintenance was considered for all three concepts. It is explained in the concept development section.

Decision matrices or similar tools are used as appropriate to organize and communicate the basis of key decisions, and the ratings used in the decision matrices are supported in the text of the report.

X Yes multiple matrixes were used to help the decision process, and they are explained in the concept development section.

The decision ‘differentiators’ are highlighted and discussed in the CD report, and are consistent with the weighted customer requirements.

X They are included in the concept development section. The decisions and rankings are explained for each matrix that was created.

The Conceptual Design Report includes a convincing case that the selected concept is worthy of support for prototype development.

X With such a small budget for our project we have come to the conclusion that our final design will meet all the customers’ needs and come closest to our budget.