Maximizing Motor Power at Constant Voltage

copy 2012 Project Lead The Way IncPrinciples Of Engineering

Speed Depends on Load Torque

When a motor is loaded with no torque it spins at no-load speed w0

w0 = no-load speed

When a motor is loaded with the stall torque tstall or more the motor will stop

tstall = stall torque

Speed vs Torque is Linear

Torque t

Spe

ed w

tstall

w0

Half speed

Stall

No-load speed

120654=minus120654120782

120649119956119957119938119949119949∙120649+120654120782

Optional slide for the geniusSpeed vs Torque Depends on Voltage

Torque t

Spe

ed w 7 V5 V

3 V

motor speed 120

motor speed 90

motor speed 60

Power

Power = Torque x Angular Speed

P = t bull w

Power = Torque x Speed

Torque t

Spe

ed w

tstall

w0

No power Why

No power Why

Maximum Power at frac12 Stall Torque

Torque t

Spe

ed w

tstall

w0

Maximum power Why

tstall

120654=minus120654120782

120649119956119957119938119949119949∙120649+120654120782

Why half stall torque

119927=[minus120654120782

120649 119956119957119938119949119949

∙120649+120654120782](120649)

119927=minus120654120782

120649119956119957119938119949119949∙120649120784+120654120782120649

120654=minus120654120782

120649119956119957119938119949119949∙120649+120654120782

Multiply both sides by torque product on left is power

Linear equation from last slide

Down-facing parabola

Torque t

Pow

er P Maximum power

Stall No load

Maximum Power at 12 Stall Torque

tstall

119927=minus120654120782

120649119956119957119938119949119949∙120649120784+120654120782120649

VEX Application Pick a Gear Ratio

Step 1 This motor is stalled What is the stall torque

Step 2 At what torque will the motor deliver maximum power

d = 3 in

F =

14 lb

VEX motor

tstall = d x F

= (3 in)(14 lb) = 42 lbin

tmaxPower = frac12 tstall

= frac12 (42 lbin) = 21 lbin

VEX Application Pick a Gear Ratio

Step 3 The same motor as in the last slide is being used to power a winch with a drum of radius 2 in lifting 02 lb What torque is the motor applying

tout = d x F

= (2 in)(02 lb) = 04 lbin

d = 2 in

F =

02 lbs

VEX Application Pick a Gear Ratio

Step 4 Instead of direct drive what gear ratio would make the motor deliver maximum power

GR =d = 2 in

F =

02 lbs

VEX Application Pick a Gear Ratio

Now the winch is geared so that the motor is delivering half its stall torque for maximum power

GR =GR =

Human Application Bicycle ldquogearsrdquo

Can you explain why changing ldquogearsrdquo on a bike helps a person win a race that goes up and down hills

References

MIT Center for Innovation in Product Development (1999) Designing with DC Motors Retrieved from httplancetmitedumotorsindexhtml

Micromo (nd) DC Motors Tutorials Retrieved from httpwwwmicromocomdc-motor-tutorialsaspx

Wikipedia (2009) Derailleur Bicycle Drivetrain Retrieved from httpenwikipediaorgwikiFileDerailleur_Bicycle_Drivetrainsvg

Speed Depends on Load Torque

When a motor is loaded with no torque it spins at no-load speed w0

w0 = no-load speed

When a motor is loaded with the stall torque tstall or more the motor will stop

tstall = stall torque

Speed vs Torque is Linear

Torque t

Spe

ed w

tstall

w0

Half speed

Stall

No-load speed

120654=minus120654120782

120649119956119957119938119949119949∙120649+120654120782

Optional slide for the geniusSpeed vs Torque Depends on Voltage

Torque t

Spe

ed w 7 V5 V

3 V

motor speed 120

motor speed 90

motor speed 60

Power

Power = Torque x Angular Speed

P = t bull w

Power = Torque x Speed

Torque t

Spe

ed w

tstall

w0

No power Why

No power Why

Maximum Power at frac12 Stall Torque

Torque t

Spe

ed w

tstall

w0

Maximum power Why

tstall

120654=minus120654120782

120649119956119957119938119949119949∙120649+120654120782

Why half stall torque

119927=[minus120654120782

120649 119956119957119938119949119949

∙120649+120654120782](120649)

119927=minus120654120782

120649119956119957119938119949119949∙120649120784+120654120782120649

120654=minus120654120782

120649119956119957119938119949119949∙120649+120654120782

Multiply both sides by torque product on left is power

Linear equation from last slide

Down-facing parabola

Torque t

Pow

er P Maximum power

Stall No load

Maximum Power at 12 Stall Torque

tstall

119927=minus120654120782

120649119956119957119938119949119949∙120649120784+120654120782120649

VEX Application Pick a Gear Ratio

Step 1 This motor is stalled What is the stall torque

Step 2 At what torque will the motor deliver maximum power

d = 3 in

F =

14 lb

VEX motor

tstall = d x F

= (3 in)(14 lb) = 42 lbin

tmaxPower = frac12 tstall

= frac12 (42 lbin) = 21 lbin

VEX Application Pick a Gear Ratio

Step 3 The same motor as in the last slide is being used to power a winch with a drum of radius 2 in lifting 02 lb What torque is the motor applying

tout = d x F

= (2 in)(02 lb) = 04 lbin

d = 2 in

F =

02 lbs

VEX Application Pick a Gear Ratio

Step 4 Instead of direct drive what gear ratio would make the motor deliver maximum power

GR =d = 2 in

F =

02 lbs

VEX Application Pick a Gear Ratio

Now the winch is geared so that the motor is delivering half its stall torque for maximum power

GR =GR =

Human Application Bicycle ldquogearsrdquo

Can you explain why changing ldquogearsrdquo on a bike helps a person win a race that goes up and down hills

References

MIT Center for Innovation in Product Development (1999) Designing with DC Motors Retrieved from httplancetmitedumotorsindexhtml

Micromo (nd) DC Motors Tutorials Retrieved from httpwwwmicromocomdc-motor-tutorialsaspx

Wikipedia (2009) Derailleur Bicycle Drivetrain Retrieved from httpenwikipediaorgwikiFileDerailleur_Bicycle_Drivetrainsvg

Speed vs Torque is Linear

Torque t

Spe

ed w

tstall

w0

Half speed

Stall

No-load speed

120654=minus120654120782

120649119956119957119938119949119949∙120649+120654120782

Optional slide for the geniusSpeed vs Torque Depends on Voltage

Torque t

Spe

ed w 7 V5 V

3 V

motor speed 120

motor speed 90

motor speed 60

Power

Power = Torque x Angular Speed

P = t bull w

Power = Torque x Speed

Torque t

Spe

ed w

tstall

w0

No power Why

No power Why

Maximum Power at frac12 Stall Torque

Torque t

Spe

ed w

tstall

w0

Maximum power Why

tstall

120654=minus120654120782

120649119956119957119938119949119949∙120649+120654120782

Why half stall torque

119927=[minus120654120782

120649 119956119957119938119949119949

∙120649+120654120782](120649)

119927=minus120654120782

120649119956119957119938119949119949∙120649120784+120654120782120649

120654=minus120654120782

120649119956119957119938119949119949∙120649+120654120782

Multiply both sides by torque product on left is power

Linear equation from last slide

Down-facing parabola

Torque t

Pow

er P Maximum power

Stall No load

Maximum Power at 12 Stall Torque

tstall

119927=minus120654120782

120649119956119957119938119949119949∙120649120784+120654120782120649

VEX Application Pick a Gear Ratio

Step 1 This motor is stalled What is the stall torque

Step 2 At what torque will the motor deliver maximum power

d = 3 in

F =

14 lb

VEX motor

tstall = d x F

= (3 in)(14 lb) = 42 lbin

tmaxPower = frac12 tstall

= frac12 (42 lbin) = 21 lbin

VEX Application Pick a Gear Ratio

Step 3 The same motor as in the last slide is being used to power a winch with a drum of radius 2 in lifting 02 lb What torque is the motor applying

tout = d x F

= (2 in)(02 lb) = 04 lbin

d = 2 in

F =

02 lbs

VEX Application Pick a Gear Ratio

Step 4 Instead of direct drive what gear ratio would make the motor deliver maximum power

GR =d = 2 in

F =

02 lbs

VEX Application Pick a Gear Ratio

Now the winch is geared so that the motor is delivering half its stall torque for maximum power

GR =GR =

Human Application Bicycle ldquogearsrdquo

Can you explain why changing ldquogearsrdquo on a bike helps a person win a race that goes up and down hills

References

MIT Center for Innovation in Product Development (1999) Designing with DC Motors Retrieved from httplancetmitedumotorsindexhtml

Micromo (nd) DC Motors Tutorials Retrieved from httpwwwmicromocomdc-motor-tutorialsaspx

Wikipedia (2009) Derailleur Bicycle Drivetrain Retrieved from httpenwikipediaorgwikiFileDerailleur_Bicycle_Drivetrainsvg

Optional slide for the geniusSpeed vs Torque Depends on Voltage

Torque t

Spe

ed w 7 V5 V

3 V

motor speed 120

motor speed 90

motor speed 60

Power

Power = Torque x Angular Speed

P = t bull w

Power = Torque x Speed

Torque t

Spe

ed w

tstall

w0

No power Why

No power Why

Maximum Power at frac12 Stall Torque

Torque t

Spe

ed w

tstall

w0

Maximum power Why

tstall

120654=minus120654120782

120649119956119957119938119949119949∙120649+120654120782

Why half stall torque

119927=[minus120654120782

120649 119956119957119938119949119949

∙120649+120654120782](120649)

119927=minus120654120782

120649119956119957119938119949119949∙120649120784+120654120782120649

120654=minus120654120782

120649119956119957119938119949119949∙120649+120654120782

Multiply both sides by torque product on left is power

Linear equation from last slide

Down-facing parabola

Torque t

Pow

er P Maximum power

Stall No load

Maximum Power at 12 Stall Torque

tstall

119927=minus120654120782

120649119956119957119938119949119949∙120649120784+120654120782120649

VEX Application Pick a Gear Ratio

Step 1 This motor is stalled What is the stall torque

Step 2 At what torque will the motor deliver maximum power

d = 3 in

F =

14 lb

VEX motor

tstall = d x F

= (3 in)(14 lb) = 42 lbin

tmaxPower = frac12 tstall

= frac12 (42 lbin) = 21 lbin

VEX Application Pick a Gear Ratio

Step 3 The same motor as in the last slide is being used to power a winch with a drum of radius 2 in lifting 02 lb What torque is the motor applying

tout = d x F

= (2 in)(02 lb) = 04 lbin

d = 2 in

F =

02 lbs

VEX Application Pick a Gear Ratio

Step 4 Instead of direct drive what gear ratio would make the motor deliver maximum power

GR =d = 2 in

F =

02 lbs

VEX Application Pick a Gear Ratio

Now the winch is geared so that the motor is delivering half its stall torque for maximum power

GR =GR =

Human Application Bicycle ldquogearsrdquo

Can you explain why changing ldquogearsrdquo on a bike helps a person win a race that goes up and down hills

References

MIT Center for Innovation in Product Development (1999) Designing with DC Motors Retrieved from httplancetmitedumotorsindexhtml

Micromo (nd) DC Motors Tutorials Retrieved from httpwwwmicromocomdc-motor-tutorialsaspx

Wikipedia (2009) Derailleur Bicycle Drivetrain Retrieved from httpenwikipediaorgwikiFileDerailleur_Bicycle_Drivetrainsvg

Power

Power = Torque x Angular Speed

P = t bull w

Power = Torque x Speed

Torque t

Spe

ed w

tstall

w0

No power Why

No power Why

Maximum Power at frac12 Stall Torque

Torque t

Spe

ed w

tstall

w0

Maximum power Why

tstall

120654=minus120654120782

120649119956119957119938119949119949∙120649+120654120782

Why half stall torque

119927=[minus120654120782

120649 119956119957119938119949119949

∙120649+120654120782](120649)

119927=minus120654120782

120649119956119957119938119949119949∙120649120784+120654120782120649

120654=minus120654120782

120649119956119957119938119949119949∙120649+120654120782

Multiply both sides by torque product on left is power

Linear equation from last slide

Down-facing parabola

Torque t

Pow

er P Maximum power

Stall No load

Maximum Power at 12 Stall Torque

tstall

119927=minus120654120782

120649119956119957119938119949119949∙120649120784+120654120782120649

VEX Application Pick a Gear Ratio

Step 1 This motor is stalled What is the stall torque

Step 2 At what torque will the motor deliver maximum power

d = 3 in

F =

14 lb

VEX motor

tstall = d x F

= (3 in)(14 lb) = 42 lbin

tmaxPower = frac12 tstall

= frac12 (42 lbin) = 21 lbin

VEX Application Pick a Gear Ratio

Step 3 The same motor as in the last slide is being used to power a winch with a drum of radius 2 in lifting 02 lb What torque is the motor applying

tout = d x F

= (2 in)(02 lb) = 04 lbin

d = 2 in

F =

02 lbs

VEX Application Pick a Gear Ratio

Step 4 Instead of direct drive what gear ratio would make the motor deliver maximum power

GR =d = 2 in

F =

02 lbs

VEX Application Pick a Gear Ratio

Now the winch is geared so that the motor is delivering half its stall torque for maximum power

GR =GR =

Human Application Bicycle ldquogearsrdquo

Can you explain why changing ldquogearsrdquo on a bike helps a person win a race that goes up and down hills

References

MIT Center for Innovation in Product Development (1999) Designing with DC Motors Retrieved from httplancetmitedumotorsindexhtml

Micromo (nd) DC Motors Tutorials Retrieved from httpwwwmicromocomdc-motor-tutorialsaspx

Wikipedia (2009) Derailleur Bicycle Drivetrain Retrieved from httpenwikipediaorgwikiFileDerailleur_Bicycle_Drivetrainsvg

Power = Torque x Speed

Torque t

Spe

ed w

tstall

w0

No power Why

No power Why

Maximum Power at frac12 Stall Torque

Torque t

Spe

ed w

tstall

w0

Maximum power Why

tstall

120654=minus120654120782

120649119956119957119938119949119949∙120649+120654120782

Why half stall torque

119927=[minus120654120782

120649 119956119957119938119949119949

∙120649+120654120782](120649)

119927=minus120654120782

120649119956119957119938119949119949∙120649120784+120654120782120649

120654=minus120654120782

120649119956119957119938119949119949∙120649+120654120782

Multiply both sides by torque product on left is power

Linear equation from last slide

Down-facing parabola

Torque t

Pow

er P Maximum power

Stall No load

Maximum Power at 12 Stall Torque

tstall

119927=minus120654120782

120649119956119957119938119949119949∙120649120784+120654120782120649

VEX Application Pick a Gear Ratio

Step 1 This motor is stalled What is the stall torque

Step 2 At what torque will the motor deliver maximum power

d = 3 in

F =

14 lb

VEX motor

tstall = d x F

= (3 in)(14 lb) = 42 lbin

tmaxPower = frac12 tstall

= frac12 (42 lbin) = 21 lbin

VEX Application Pick a Gear Ratio

Step 3 The same motor as in the last slide is being used to power a winch with a drum of radius 2 in lifting 02 lb What torque is the motor applying

tout = d x F

= (2 in)(02 lb) = 04 lbin

d = 2 in

F =

02 lbs

VEX Application Pick a Gear Ratio

Step 4 Instead of direct drive what gear ratio would make the motor deliver maximum power

GR =d = 2 in

F =

02 lbs

VEX Application Pick a Gear Ratio

Now the winch is geared so that the motor is delivering half its stall torque for maximum power

GR =GR =

Human Application Bicycle ldquogearsrdquo

Can you explain why changing ldquogearsrdquo on a bike helps a person win a race that goes up and down hills

References

MIT Center for Innovation in Product Development (1999) Designing with DC Motors Retrieved from httplancetmitedumotorsindexhtml

Micromo (nd) DC Motors Tutorials Retrieved from httpwwwmicromocomdc-motor-tutorialsaspx

Wikipedia (2009) Derailleur Bicycle Drivetrain Retrieved from httpenwikipediaorgwikiFileDerailleur_Bicycle_Drivetrainsvg

Maximum Power at frac12 Stall Torque

Torque t

Spe

ed w

tstall

w0

Maximum power Why

tstall

120654=minus120654120782

120649119956119957119938119949119949∙120649+120654120782

Why half stall torque

119927=[minus120654120782

120649 119956119957119938119949119949

∙120649+120654120782](120649)

119927=minus120654120782

120649119956119957119938119949119949∙120649120784+120654120782120649

120654=minus120654120782

120649119956119957119938119949119949∙120649+120654120782

Multiply both sides by torque product on left is power

Linear equation from last slide

Down-facing parabola

Torque t

Pow

er P Maximum power

Stall No load

Maximum Power at 12 Stall Torque

tstall

119927=minus120654120782

120649119956119957119938119949119949∙120649120784+120654120782120649

VEX Application Pick a Gear Ratio

Step 1 This motor is stalled What is the stall torque

Step 2 At what torque will the motor deliver maximum power

d = 3 in

F =

14 lb

VEX motor

tstall = d x F

= (3 in)(14 lb) = 42 lbin

tmaxPower = frac12 tstall

= frac12 (42 lbin) = 21 lbin

VEX Application Pick a Gear Ratio

Step 3 The same motor as in the last slide is being used to power a winch with a drum of radius 2 in lifting 02 lb What torque is the motor applying

tout = d x F

= (2 in)(02 lb) = 04 lbin

d = 2 in

F =

02 lbs

VEX Application Pick a Gear Ratio

Step 4 Instead of direct drive what gear ratio would make the motor deliver maximum power

GR =d = 2 in

F =

02 lbs

VEX Application Pick a Gear Ratio

Now the winch is geared so that the motor is delivering half its stall torque for maximum power

GR =GR =

Human Application Bicycle ldquogearsrdquo

Can you explain why changing ldquogearsrdquo on a bike helps a person win a race that goes up and down hills

References

MIT Center for Innovation in Product Development (1999) Designing with DC Motors Retrieved from httplancetmitedumotorsindexhtml

Micromo (nd) DC Motors Tutorials Retrieved from httpwwwmicromocomdc-motor-tutorialsaspx

Wikipedia (2009) Derailleur Bicycle Drivetrain Retrieved from httpenwikipediaorgwikiFileDerailleur_Bicycle_Drivetrainsvg

Why half stall torque

119927=[minus120654120782

120649 119956119957119938119949119949

∙120649+120654120782](120649)

119927=minus120654120782

120649119956119957119938119949119949∙120649120784+120654120782120649

120654=minus120654120782

120649119956119957119938119949119949∙120649+120654120782

Multiply both sides by torque product on left is power

Linear equation from last slide

Down-facing parabola

Torque t

Pow

er P Maximum power

Stall No load

Maximum Power at 12 Stall Torque

tstall

119927=minus120654120782

120649119956119957119938119949119949∙120649120784+120654120782120649

VEX Application Pick a Gear Ratio

Step 1 This motor is stalled What is the stall torque

Step 2 At what torque will the motor deliver maximum power

d = 3 in

F =

14 lb

VEX motor

tstall = d x F

= (3 in)(14 lb) = 42 lbin

tmaxPower = frac12 tstall

= frac12 (42 lbin) = 21 lbin

VEX Application Pick a Gear Ratio

Step 3 The same motor as in the last slide is being used to power a winch with a drum of radius 2 in lifting 02 lb What torque is the motor applying

tout = d x F

= (2 in)(02 lb) = 04 lbin

d = 2 in

F =

02 lbs

VEX Application Pick a Gear Ratio

Step 4 Instead of direct drive what gear ratio would make the motor deliver maximum power

GR =d = 2 in

F =

02 lbs

VEX Application Pick a Gear Ratio

Now the winch is geared so that the motor is delivering half its stall torque for maximum power

GR =GR =

Human Application Bicycle ldquogearsrdquo

Can you explain why changing ldquogearsrdquo on a bike helps a person win a race that goes up and down hills

References

MIT Center for Innovation in Product Development (1999) Designing with DC Motors Retrieved from httplancetmitedumotorsindexhtml

Micromo (nd) DC Motors Tutorials Retrieved from httpwwwmicromocomdc-motor-tutorialsaspx

Wikipedia (2009) Derailleur Bicycle Drivetrain Retrieved from httpenwikipediaorgwikiFileDerailleur_Bicycle_Drivetrainsvg

Torque t

Pow

er P Maximum power

Stall No load

Maximum Power at 12 Stall Torque

tstall

119927=minus120654120782

120649119956119957119938119949119949∙120649120784+120654120782120649

VEX Application Pick a Gear Ratio

Step 1 This motor is stalled What is the stall torque

Step 2 At what torque will the motor deliver maximum power

d = 3 in

F =

14 lb

VEX motor

tstall = d x F

= (3 in)(14 lb) = 42 lbin

tmaxPower = frac12 tstall

= frac12 (42 lbin) = 21 lbin

VEX Application Pick a Gear Ratio

Step 3 The same motor as in the last slide is being used to power a winch with a drum of radius 2 in lifting 02 lb What torque is the motor applying

tout = d x F

= (2 in)(02 lb) = 04 lbin

d = 2 in

F =

02 lbs

VEX Application Pick a Gear Ratio

Step 4 Instead of direct drive what gear ratio would make the motor deliver maximum power

GR =d = 2 in

F =

02 lbs

VEX Application Pick a Gear Ratio

Now the winch is geared so that the motor is delivering half its stall torque for maximum power

GR =GR =

Human Application Bicycle ldquogearsrdquo

Can you explain why changing ldquogearsrdquo on a bike helps a person win a race that goes up and down hills

References

MIT Center for Innovation in Product Development (1999) Designing with DC Motors Retrieved from httplancetmitedumotorsindexhtml

Micromo (nd) DC Motors Tutorials Retrieved from httpwwwmicromocomdc-motor-tutorialsaspx

Wikipedia (2009) Derailleur Bicycle Drivetrain Retrieved from httpenwikipediaorgwikiFileDerailleur_Bicycle_Drivetrainsvg

VEX Application Pick a Gear Ratio

Step 1 This motor is stalled What is the stall torque

Step 2 At what torque will the motor deliver maximum power

d = 3 in

F =

14 lb

VEX motor

tstall = d x F

= (3 in)(14 lb) = 42 lbin

tmaxPower = frac12 tstall

= frac12 (42 lbin) = 21 lbin

VEX Application Pick a Gear Ratio

Step 3 The same motor as in the last slide is being used to power a winch with a drum of radius 2 in lifting 02 lb What torque is the motor applying

tout = d x F

= (2 in)(02 lb) = 04 lbin

d = 2 in

F =

02 lbs

VEX Application Pick a Gear Ratio

Step 4 Instead of direct drive what gear ratio would make the motor deliver maximum power

GR =d = 2 in

F =

02 lbs

VEX Application Pick a Gear Ratio

Now the winch is geared so that the motor is delivering half its stall torque for maximum power

GR =GR =

Human Application Bicycle ldquogearsrdquo

Can you explain why changing ldquogearsrdquo on a bike helps a person win a race that goes up and down hills

References

MIT Center for Innovation in Product Development (1999) Designing with DC Motors Retrieved from httplancetmitedumotorsindexhtml

Micromo (nd) DC Motors Tutorials Retrieved from httpwwwmicromocomdc-motor-tutorialsaspx

Wikipedia (2009) Derailleur Bicycle Drivetrain Retrieved from httpenwikipediaorgwikiFileDerailleur_Bicycle_Drivetrainsvg

VEX Application Pick a Gear Ratio

Step 3 The same motor as in the last slide is being used to power a winch with a drum of radius 2 in lifting 02 lb What torque is the motor applying

tout = d x F

= (2 in)(02 lb) = 04 lbin

d = 2 in

F =

02 lbs

VEX Application Pick a Gear Ratio

Step 4 Instead of direct drive what gear ratio would make the motor deliver maximum power

GR =d = 2 in

F =

02 lbs

VEX Application Pick a Gear Ratio

Now the winch is geared so that the motor is delivering half its stall torque for maximum power

GR =GR =

Human Application Bicycle ldquogearsrdquo

Can you explain why changing ldquogearsrdquo on a bike helps a person win a race that goes up and down hills

References

MIT Center for Innovation in Product Development (1999) Designing with DC Motors Retrieved from httplancetmitedumotorsindexhtml

Micromo (nd) DC Motors Tutorials Retrieved from httpwwwmicromocomdc-motor-tutorialsaspx

Wikipedia (2009) Derailleur Bicycle Drivetrain Retrieved from httpenwikipediaorgwikiFileDerailleur_Bicycle_Drivetrainsvg

VEX Application Pick a Gear Ratio

Step 4 Instead of direct drive what gear ratio would make the motor deliver maximum power

GR =d = 2 in

F =

02 lbs

VEX Application Pick a Gear Ratio

Now the winch is geared so that the motor is delivering half its stall torque for maximum power

GR =GR =

Human Application Bicycle ldquogearsrdquo

Can you explain why changing ldquogearsrdquo on a bike helps a person win a race that goes up and down hills

References

MIT Center for Innovation in Product Development (1999) Designing with DC Motors Retrieved from httplancetmitedumotorsindexhtml

Micromo (nd) DC Motors Tutorials Retrieved from httpwwwmicromocomdc-motor-tutorialsaspx

Wikipedia (2009) Derailleur Bicycle Drivetrain Retrieved from httpenwikipediaorgwikiFileDerailleur_Bicycle_Drivetrainsvg

VEX Application Pick a Gear Ratio

Now the winch is geared so that the motor is delivering half its stall torque for maximum power

GR =GR =

Human Application Bicycle ldquogearsrdquo

Can you explain why changing ldquogearsrdquo on a bike helps a person win a race that goes up and down hills

References

MIT Center for Innovation in Product Development (1999) Designing with DC Motors Retrieved from httplancetmitedumotorsindexhtml

Micromo (nd) DC Motors Tutorials Retrieved from httpwwwmicromocomdc-motor-tutorialsaspx

Wikipedia (2009) Derailleur Bicycle Drivetrain Retrieved from httpenwikipediaorgwikiFileDerailleur_Bicycle_Drivetrainsvg

Human Application Bicycle ldquogearsrdquo

Can you explain why changing ldquogearsrdquo on a bike helps a person win a race that goes up and down hills

References

MIT Center for Innovation in Product Development (1999) Designing with DC Motors Retrieved from httplancetmitedumotorsindexhtml

Micromo (nd) DC Motors Tutorials Retrieved from httpwwwmicromocomdc-motor-tutorialsaspx

Wikipedia (2009) Derailleur Bicycle Drivetrain Retrieved from httpenwikipediaorgwikiFileDerailleur_Bicycle_Drivetrainsvg

References

MIT Center for Innovation in Product Development (1999) Designing with DC Motors Retrieved from httplancetmitedumotorsindexhtml

Micromo (nd) DC Motors Tutorials Retrieved from httpwwwmicromocomdc-motor-tutorialsaspx

Wikipedia (2009) Derailleur Bicycle Drivetrain Retrieved from httpenwikipediaorgwikiFileDerailleur_Bicycle_Drivetrainsvg