BLOODHOUND1000mph Land Speed Record

Group 32 –Project 3

BACKGROUND

The land speed record is the highest speed achieved by a person using a vehicle on land.

The United Kingdom, with the exception of one year, held the record between 1914 and 1963 until the United States took over and continually improved it.

The UK was rapidly losing its reputation as an industrial giant in the world and the loss of the land speed record was seen as another national humiliation.

Acting against the tide of faltering national technological and manufacturing prowess were the actions and motivations of a public schooled army officer’s son, Richard Noble. UK national pride was at stake and it needed a special person to challenge the USA and return to the top of the record books.

Against all odds, with the UK nation despondently thinking it had dropped off the leader board of technological nations forever, Richard wrestled the record back from the USA driving the vehicle “THRUST 2” to 633.47 mph himself in October 1983.

2

National pride was restored to a degree. Modelling data after the actual record run showed that if THRUST 2 had achieved another 6mph the car would have been airborne, disaster probably would have occurred, and Richard Noble may have been at risk of losing his life.

Undisturbed by this near death experience, Richard planned to beat the sound barrier in a car. He achieved this on October 15 1997 in THRUST SSC, although not driving this time, by achieving 763.035 mph. The driver was Andy Green, double first in Mathematics at Cambridge University, RAF fighter jet pilot, and keen at his job.

Although exhausted by the challenge processes, particularly financing the venture, Richard approached his aerodynamic guru, Ron Ayers to enquire if a car could achieve twice the speed of sound. Ron stated that Mach 1.4 (1065 mph) is the aerodynamic limit. Ron was then asked if 1000mph would be possible and he replied barely probable. This was enough to spark a new challenge for Richard, resulting in a new project “Bloodhound” was born. Andy Green was again asked if he would like to drive which he gladly accepted.

The Bloodhound project counters UK culture’s lack of confidence in technology, engineering, manufacturing, computer services and project management. As a result, the UK Government has offered the most technologically advanced aero jet engine produced in this country (Rolls Royce EJ200) and access to the European Space Agency’s next generation (Nammo) hybrid rocket in return for inspiring education.

3

The Bloodhound project is most strikingly different than other Land Speed Record attempts due to its emphasis on computer modelling and it’s data acquisition. This enables the production of computer simulation “in silico” experimentation. This is aimed to reduce/ eliminate the need to guess, over engineer, be lucky and trusting intuition in the build process.

WHY DO IT? Humans are obsessed with speed. Who hasn’t taken their car, motorbike, bicycle, athletic achievement to a limit above ‘safe”. Who wouldn’t want to commute to work at 1000 mph? Who doesn’t want to see a car go faster than a single bullet? (We are in Superman territory here). This is the stuff of legend and its associated benefits of national pride and inspiration. It should be noted that the USA, USA & Canada jointly, Australia and New Zealand are all attempting to reach this summit of technology while Bloodhound is developing. In everything the rest of the World like to beat the UK so the competition is real.

4

INTRODUCTIONThe task is to produce an Excel simulation of the Bloodhound land-speed record.

The brief is to demonstrate the car reaching 1000 mph within the regulation test distance of 4.5 to 5.5 miles and stopping safely within 12 miles.

The information is of interest to the project as it explains the car’s record attempt in mathematical terms. Forces can be calculated at different points of the model to determine stresses and strains acting on the car.

The Bloodhound website shows the “Perfect Run” in graphical form. The vehicle is shown in the graph travelling at only 100 mph in the first 17 seconds. Bloodhound is required to start slowly to avoid mud and dust being thrown up and into the air intake for the EJ200 Jet engine (Bloodhound website). We were unable to replicate this low speed and achieve the record speed. External advice was sought without success and an email was sent to JohnLanham @ UWE for advice but no reply was received.

5

ASSUMPTIONS and DATA COLLECTION.The Bloodhound project is to exceed 1000mph and claim a new land speed record. It is also to educate and inspire the next generation of engineers. Data has been collected from the official Bloodhound website which supplies large amounts of information.

1. Mass

Mass is variable due to a fuel load of approximately 1500kg. Assume consumption at a constant rate. Some Jet fuel is required to turn the car around for the second run. This action will also increase engine cooling time and was adopted as the best solution. Suggested by Rolls Royce engineers. (Bloodhound).

Mass is as per the Bloodhound website (11- 4 - 2016) “Design condition, full with fluids and driver” at 7786kg. Empty of fluids but including driver the mass is 6227kg. The car is presented as weighing over 7,500kg in media presentations. The design target mass is lower but there is no evidence to suggest the car’s mass is less than the design condition given.

6

2. Air Density

Equation for air density:

Rho (air density) = Pressure(pascals)

Rspecific(Specific gas constant) x T (absolute temp (k) )

Pressure Range

mb

915-940

Typical limits of SA surface pressure

Ambient Air Pressure range

mb

970-1040

Typical limits of UK surface pressure

Figure A.

Figure A shows a comparison of the South African (Hakskeen Pan) and UK ambient air pressure ranges.

Altitude of Hakskeen Pan is 794m above sea level. Air pressure reduces with altitude.

The temperature ranges due not vary greatly. According to Ron Ayers and Steve Newey of Bloodhound, in a very preliminary look, it suggested that top speed could be increased by 1 mph if the temperature is reduced by 1-degree C. Air density is inversely proportional to temperature and therefore also inversely proportional to the Drag.

The temperature on the Record Run day will be as low as possible and ideally lower than the 15C shown in the 1.225kg/m3 calculation.

7

As there is no specific date given for the run, climatic conditions have too much variance to suggest an Air Density calculation as an alternative to the 1.225kg/m3 given however it is expected to be less as in Bloodhound’s media presentations.

Assume air density (rho ) = 1.225kg/m3

3. Rolling Resistance.

The rolling resistance remained constant due to the variation in the track surface and the need to steer the car using the wheels as aerodynamic devices. When the wheels are at an angle and in contact with the track the rolling resistance is increased.The surface of the track is a natural mud layer on bedrock. The thickness of the mud varies so the frictional forces will vary with inconsistencies of the surface and the possibility of the wheels touching bedrock. Rolling Resistance will contribute 11% of the braking force. (Bloodhound) Over 900 mph the shock wave effects will have a reduction on the rolling resistance at the wheels giving a skating feel to the driver. (Bloodhound)Supersonic aerodynamic effects are ignored due to complexity of calculations. i.e. Krr v = Zero.

Assume Rolling Resistance is constant throughout journey.

8

4. Thrust- Jet and Rocket.

The engine data was acquired from the Bloodhound website. The website reports that it is necessary for the car to start slowly as this will avoid disturbed surface elements being accelerated into the jet engine inlet. Any contaminants in the engine could affect its performance.

The Rocket engine can run for 20 seconds before all fuel is spent. (Bloodhound)

The Perfect Run states the need to throttle back the jet engine showing a degree of driver choice to achieve run requirements.

5. Drag coefficient

Frontal area figures are taken from the Bloodhound website as 1.937 m2.

The drag coefficient is shown on the Bloodhound website as 1.32.The Cd of 1.937 figure given refers to Area * Cd = 1.32.Therefore, Cd = 1.32/ 1.937 = 0.6815.

9

This is a high figure compared with other vehicle types however Bloodhound expect 52% of the braking to come from aerodynamic drag.

6. Braking

Bloodhound’s ability to reduce speed is a safety as well as a performance factor.

As mentioned above 52% of negative Thrust will come from Aerodynamic Drag and 11% from Rolling Resistance. (Bloodhound)

Air brakes are controllable by the driver and when fully extended have the aerodynamic effect of doubling Area and Drag coefficient. (Bloodhound).

A parachute with a diameter of 2m (Bloodhound) can be deployed by the driver at below 650 mph. The Drag coefficient of 0.51 was given.

Wheel brakes are also controllable by the driver and can be deployed below 200 mph.

Braking coefficients have been chosen to remain below 3g for the model. In reality the driver has a great deal of control over the braking process to reflect real life events.

Driver safety is the paramount concern over ALL other factors. The braking capabilities are within parameters for all predicted eventualities. For example, the vehicle will be stop within 12 miles by using a braking combination of air/vehicle, parachute/ vehicle, or air/parachute (Bloodhound).

10

In a perfect run the driver will have options to make the run more comfortable for himself by removing g-forces and/or to allow for the best possible engine recovery scenarios e.g. both engines will need to cool down prior to preparation for the return run.

Part of Andy Green’s, Bloodhound’s driver routine during the run is to counteract g-forces by exercising different muscle groups. As an ex fighter jet pilot and a current acrobatic plane pilot he has no difficulty coping with 3g physiological stresses and they are well within his personal limits. He is able to regularly fly the acceleration pattern of the record run in his acrobatic plane to practice and acclimatize his body. (Bloodhound)

7. Wind.

Assume there is zero wind.

8. General

The test area of 4.5 to 5.5 miles is puzzling as the course is 12 miles long. Bloodhound is required to turnaround and complete the course from the opposite direction within one hour. The original starting point is 12 miles away so if Bloodhound was to begin the return journey the measured mile would be at 6.5 to 7.5 miles and the car would need to stop in 4.5 miles. If the measured mile was to alter position between runs this could alleviate the problem but I doubt that sensitive recording equipment set up to record an historic event with the goal so close to the emotive 1000 mph would want to be moved.

11

On the Bloodhound website “the sound of Bloodhound SSC” a 1000 mph run shows the measured mile at the midpoint i.e. 5.5 – 6.5 miles on 17 June 2014.

MODEL

Newton’s Second Law states that the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, and inversely proportional to the mass of the object.

This is represented by the equation F = mass * acceleration.

The net forces are the Tjet and Trocket acting in a positive direction with Aerodynamic Drag and Rolling Resistance (sonic and subsonic) acting in a negative direction.

Fnet = Tjet + Trocket – 0.5*Cd*A*Rho*v^2 – mgCrr – krrv

As shown above Fnet = ma so:

Thrust – Drag – Rolling Resistance = m * a

Rearranging for acceleration:

a = (Thrust – Drag – Rolling Resistance) / m

12

Elements of Model

Thrust = Tjet + Trocket

Tjet (maximum) = 60kN to 90kN (with afterburner applied) [Bloodhound]

Trocket (maximum) = 122kN (Bloodhound)

Cd = Drag coefficient = 0.6815 (no units) (Bloodhound)

A = 1.937 m2 (Bloodhound)

Rho = 1.225 kg/m3 (Given in question)

V = velocity (varies) (m/s)

m = Mass of vehicle, fuel, and driver. = 7786 kg reduces as fuel consumed. (Bloodhound)

g = gravitational force at earth’s surface = 9.81 m/s2

Crr - Rolling resistance

1200N(given) = 7786 * 9.81 * Crr

Crr= 1200 / (7786 *9.81)

Crr = 0.0157(no units).

13

SI units are used in all cases but converted to imperial to give historical comparison with former records.

EXCEL SOLUTIONS

For ease of comparison all five graphs (figures 1,2,3,4, and 5) have the time period for the horizontal axis representing the 120 seconds (2 minutes).

Figure 1 : Bloodhound Record Run acceleration/ time graph.

14

0 20 40 60 80 100 120 140

-40

-30

-20

-10

0

10

20

30

a (m/s2) v t (s)

Time (seconds)

Acc

eler

atio

n (m

/s2)

In figure 1 Bloodhound’s acceleration peaks at 25 m/s/s and troughs at -29.6 m/s/s.The stepping of acceleration values from the start (time =0) is due to an increase in thrust to the jet engine followed by the afterburner being turned on resulting in a further increase in thrust.The acceleration then reduces due to the increase of aerodynamic drag by the increased resultant velocity.The Rocket Engine is then switched on causing an instantaneous increase in acceleration to the maximum of 25 m/s/s. The Aerodynamic Drag reduces the acceleration to 0.5g over time.The Rocket Engine is then turned off causing an instantaneous loss of thrust. The Jet Engine is turned off 1 second later resulting in zero thrust to Bloodhound. The Aerodynamic Drag at the measured mile peak velocity stage at 179839 N. This large negative thrust causes a large change in acceleration in the negative direction to – 30 m/s/s.The Aerodynamic Drag is dependent on velocity squared. Therefore, as velocity is reduced by acceleration in the negative direction so does the Aerodynamic Drag reduce to – 16.5 m/s/s.The Air brakes are applied at 750mph which increases the frontal surface area by a factor determined by the driver (up to doubling the

15

original area) which is a factor of Aerodynamic Drag. A resultant increase in negative acceleration to -21.7 m/s/s is achieved. The drop in velocity causes the acceleration in the negative direction reducing as before.At around 550 mph at 49.4 seconds the parachute is opened. This adds a further addition to the frontal surface area resulting in increasing Aerodynamic Drag which increases acceleration in the negative direction from -12.1 m/s/s to –22.8 m/s/s.With Air Brakes functioning and driver controllable, the parachute inflated, Bloodhound is in a controlled deceleration to the finish. As there is zero thrust the driver uses the vehicle wheel brakes to bring Bloodhound to rest at the required point. The smooth long curve of the graph in the final section reflects this control

Figure 2 : Bloodhound Record Run velocity/ time graph.

0 20 40 60 80 100 120 140-200

0

200

400

600

800

1000

1200

v (mph) v t (s)

Time (seconds)The area between the two bold vertical lines is at a distance of 4.5 miles and 5.5 miles.

This represents the measured mile area for the final analysis.

Velo

city

(mph

)

Figure 2 shows Bloodhounds velocity against time. The two bold vertical lines represent the measured mile. Bloodhound is required in

16

the Record Run to reach an average of 1000 mph during the measured mile section.A straight line would reflect constant acceleration. As we have seen in the figure 1 (acceleration) analysis the acceleration varies with thrust in a positive direction and by velocity and surface area in the negative direction.The rocket and jet engines are switched off and within the measured mile section. The Aerodynamic Drag (52%) and Rolling Resistance (11%) are designed to contribute to braking performance.The remaining braking is controlled by the driver to produce a smooth velocity reduction enough to roll to the finish line.

Figure 3 : Bloodhound Record Run distance/ time graph

0 20 40 60 80 100 120 1400.0

2.0

4.0

6.0

8.0

10.0

12.0

Distance (miles) v t (s)

Time (seconds)

Dist

ance

(mile

s)

17

Figure 3 shows the distance travelled from the start by time. A straight line would show constant velocity. The velocity varies to the acceleration changes due to the changes in thrust and aerodynamic drag. Ideally Bloodhound would finish at the 12 mile mark.The acceleration graph (figure 1) was deliberately formed to achieve 1000 mph average velocity within the measured mile and to apply the air brakes and parachute early in case of failure.

Andy Green’s first option is the air brakes which are independently hydraulically operated. They could have been applied earlier/ later/ opened more / opened less or not at all in the event of total failure.

Andy’s next option is when to use the parachute which will be dependent on the air brake functionality and the agreed ideal stress parameters on the system. He will want to apply the parachute to reduce the stress on vehicle brakes but not too early otherwise the vehicle will not reach the finish at 12 miles.

Arriving at the 12-mile point is an important task for Andy to achieve.At the finish many support crew will be waiting to prepare the car for its compulsory second run. Recovering the vehicle would waste valuable time.

The Jet engine could be restarted to provide thrust but this would not be a preferred option as a major problem for the support crew is reducing engine temperatures to enable working and refueling.

18

Figure 4 : Bloodhound Record Run mass/ time graph

0 20 40 60 80 100 120 1400

100020003000400050006000700080009000

Bloodhound mass (kg) v t (s)

Time (seconds)

Mas

s (k

g)

In figure 4 mass is shown as decreasing during the run.This is to reflect Bloodhound using stored fuel to power the rocket and jet engines.

19

The Rocket fuel has three elements: HTP (H2O2) Oxidant, HTPB Fuel, and HTP Propellant. The total consumed mass is shown as 963kg Oxidant, 181kg Fuel, and 776kg Propellant = 1920 kg (total consumed). Some Propellant mass not included in the above figures is not consumed as it is required to prevent the pumps from running dry. This mass is included in the dry car mass.By comparison the EJ200 Rolls Royce jet engine has a total fuel mass of 302 kg for a Record Run time of 39 seconds with some left over to turn Bloodhound around for its second run.An internal combustion supercharged Jaguar V8 engine has replaced the Cosworth V8 Formula engine to pump Oxidant into the rocket engine. This engine runs on unleaded fuel for the 20 seconds of operation. The unleaded fuel mass is not given on the Bloodhound website for either engines. The engine needs to run at 18000 rpm to pump the oxidant quick enough but only for the 20 seconds and is therefore likely to be a relatively small mass. This fuel consumption and its effect on overall mass has not been considered.

Figure 5: Bloodhound Record Run Aerodynamic Drag + Rolling Resistance/ time graph.

20

0 20 40 60 80 100 120 1400.0

20000.040000.060000.080000.0

100000.0120000.0140000.0160000.0180000.0200000.0

Aerodynamic Drag + Rolling Resistance (N) v t (s)

Time (seconds

Cd a

nd R

R (N

)

In figure 5. Aerodynamic Drag and Rolling Resistance peaks at 180000 N as shown. This is why Ron Ayers, Bloodhound aerodynamic expert stated that Mach 1.4, around 1065 mph is the maximum velocity for a wheeled vehicle.The drag increases with velocity until the velocity peaks at 1052.4 mph. Due to thrust being reduced and within a second completely stopped an acceleration in the negative direction occurs. Velocity and Drag reduces as a result until at at 44 seconds the air brakes are turned on. They have variable frontal area increase capability and drag is increased. With zero thrust and only acceleration in the negative direction possible (and planned for) the resultant velocity reduction factor becomes larger than the surface area increase factor and the drag reduces again until the parachute is deployed at 49.4 seconds.The drag immediately is increased due to the increase in frontal surface area given by the parachute. Zero thrust, positive drag and

21

positive rolling resistance means the acceleration continues in the negative direction. The resultant reduction in velocity also reduces drag until the vehicle brakes are used to “fine tune” the drag by increasing rolling resistance under the full control of the driver.

SUMMARYThe Bloodhound project was of vague interest prior to this exercise.

Using a mathematical model and observing the effect of quantifying values to a variable has been an adventure.

The adventure aspects of the project as a whole, the honorable pursuit of promoting education and awareness, the personal risk to life from the participants, and the good news selling of a “better Britain” are all positive.

The project has been subject to considerable time delays from 2012 to sometime this year.

As mentioned in the background section in this document the project has been extensively computer modelled. Our results differ from the Perfect Run despite our best efforts. With more data at their disposal

22

creating better computational fluid dynamic modelling it would be very interesting to see how Bloodhound achieved their velocity/ acceleration Perfect Run graph.

As some data on the website is from 2012 there is a need to update it to give more confidence to our modelling. The mass variables in particular would be of interest.

Experimental data to confirm the model would also be welcome.

We are confident that the project will be successful in beating the 1000mph barrier and eagerly look forward to the day of the run.

REFERENCES.

Bloodhound. (2012). Vehicle technical specifications. Available: http://www.bloodhoundssc.com. Last accessed 12th April 2016.

BloodhoundSSC. (2012). The team. Available: http://www.bloodhoundssc.com. Last accessed 12 April 2016.

Green, Andy. (2013). FIA World Speed record.. Available: http://www.bloodhoundssc.com. Last accessed 12 April 2016.

BloodhoundSSC. (2012). The Perfect Run. Available: http://www.bloodhoundssc.com. Last accessed 12 April 2016.

Noble, Richard. (2008). The Adventure. Available: http://www.bloodhoundssc.com. Last accessed 12 April 2016.

23

Wing Commander Greene, Nic. (2012). Physiological effects of driving Bloodhound. Available: http://www.bloodhoundssc.com. Last accessed 12 April 2016.

Green, Andy. (2012). Training for 1000 mph. Available: http://www.bloodhoundssc.com. Last accessed 12 April 2016.

Green, Andy. (2012). The challengers. Available: http://www.bloodhoundssc.comp. Last accessed 12 April 2016.

24