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Calculating acceleration on different gears in vehicle

  1. Oct 18, 2013 #1
    Acceleration is not Force/mass, mechanical advantage (?)

    I have a vehicle with wheels and electric motor that drives that wheels.
    Those are characteristics of engine

    Resultant torque and velocity at wheel will depend on radius of that wheel, as wheel work as gearing.
    Let's say i will try with wheel A of 1m radius and wheel B of 2m radius.
    On same engine speed vehicle with wheel A will have bigger torque&force at wheel but with lower wheel velocity, opposite will be on wheel B.
    But the acceleration force will be same, as it depends on power from engine.

    This guy called newton said that acceleration is force/mass. But he is liar as its not possible.
    Because in my example on wheel A force is two times bigger than in Wheel B, but both vehicles have same acceleration at same engine revs.

    Also look here:
    this picture is from https://en.wikipedia.org/wiki/Mechanical_advantage article

    On Both bikes same force and power is applied on pedal,
    the difference is gearing of the bikes. Bike on the left is making twice force/torque bike on right but on two times shorter distance which means two times smaller wheel speed.
    Both bicycles encounter same acceleration. If i was using newton's incorrect calculating of acceleration bike on left would have bigger acceleration. Also, i could have infinite acceleration with proper gearing...

    How to calculate real acceleration? I can't just multiple force with distance or wheel velocity. What when the bike is stopped and i start to apply force on pedal? the wheel's speed and distance is 0 so would be the acceleration

    I know now that wheel and gearing are machines that use Mechanical Advantage
    And wheel size and gearing is just converting between more/less torque and more/less velocity of wheel (distance)
    The power is the same, and actually acceleration is same too

    but how to calculate acceleration if i know engine torque, revs, gearing, wheel diameter, wheel velocity
    take in mind that the wheel velocity can be 0 (when vehicle is stopped)
    also, engine can also be stopped as its electrical dc engine that is able to produce torque at 0 rpm

    look at this too:

    those are torques on wheel and rpm on wheels on different gears
    we all know that its the power that actually accelerates vehicle
    but stupid Newton tells me that its the force/torque
    if he was right i could use such gearing that would make 1000000 torque on wheel from engine that generates 1 Watt and i would have unreal acceleration

    as i told, can't just multiply torque with distance/velocity as vehicle and engine can be stopped
    Last edited: Oct 19, 2013
  2. jcsd
  3. Oct 19, 2013 #2


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    torque is not force. Unit of force is Newton. Unit of torque is Newton-Meter. Torque is force times distance. So your leverage needs to be part of your acceleration calculation.
  4. Oct 19, 2013 #3
    force times distance? the distance is wheel diameter,
    WHAT if i use same wheel size but i attach differential/gear to my engine
    speed torque engine_rpm wheel_rpm
    vehicle A 10 100 200 50
    vehicle B 20 100 400 100

    torque is same but vehicle B is applying DOUBLE the power of A
    and the acceleration is double
    but forces are same

    imagine same cars
    they generate 300 torque but the second car is at double rotational speed than the first
    the torque and force at wheel are same, but the second car is having double speed

    if we ignore friction/air/drivetrain deceleration, what we get:
    the second one is accelerating two times faster even that torque is same

    what is gear doing? it can half the torque but double rotational speed
    or opposite, double torque but half rotational speed

    in each case power and resulting ACCELERATION is same
    but forces on wheels is different
    and the distance that force is applying on
    and wheel velocity

    but stupid newton theory is not saying anything about it
    it just says force/mass is acceleration which is ********

    if that was true i would make a gearing that would generate 500000 torque and force from 1 Watt engine and it would accelerate as hell even if it weights 1000 kg

    also, even on same gear
    imagine an engine that generate same torque on all rotational speeds
    so i could drive 2000 rpm with 1000 torque and then 4000 rpm with 1000 torque
    FORCE ON WHEEL AND WHEELSPIN RISK would be SAME in both situations
    but at 4000rpm power would be double and so the acceleration

    but can't just multiple torque times rotational speed
    because engine and vehicle can be stalled
    and now i generate torque
    power is 0
    but the vehicle has to move

    can't just multiple torque with gearing. because gearing is same when 1000 rpm and 2000 rpm on same gear, but on 2000rpm power is double

    maybe i should do somethin like this
    torque * (1.0+distance_in_metres_travelled_by_wheel) = acceleration
    but i need scientific basics to calculate acceleration

    also imagine this:
    you are on bicycle with eletrical motor
    this motor generates constant 100 Watts of power
    so the acceleration is same on all rpms, 100, 1000, 10000
    but the torque is diminishing, SO IS THE CHANCE TO WHEELSPIN
    you can easily wheelspin when starting or raise front wheel
    but can't when big speed

    also, HOW IS THE ACCELERATION SAME when force is diminishing with speed
  5. Oct 19, 2013 #4
    Look at this picture
    its from https://en.wikipedia.org/wiki/Mechanical_advantage_device article

    compare first and fourth pulley
    the fourth have only 25N applied but its generating same force and acceleration as 100N in first pulley
    I KNOW WORK and energy are same

    but the fact is first and fourth pulley have different forces applied but same acceleration and power
    but stupid newton says that acceleration is DIRECTLY proportionally to force and inversely to mass
    he havent said a word about force over distance

    i can't just multiple force with distance
    because what if there is no distance at all?
    for example imagine this pulley, lets say this weight on bottom is heavy and it stays on floor
    now i apply force but this force is too small to overcome gravity
    so there is no movement
  6. Oct 19, 2013 #5
    I'm dying of laughter right now. :rofl:

    Force and torque are not the same thing.
  7. Oct 19, 2013 #6
    The force on wheels is torque on wheel divided by wheel radius

    Don't even try to suggest that car on higher gears generate same force on wheels (assuming same engine rpm and power is present). The higher gear the less force -> its very easy to wheel spin at first gear if you press pedal to floor but its very hard to wheel spin at 3rd gear when pedal pressed to floor
    and if we ignore deceleration forces like air/rolling/drivetrain losses
    that car would accelerate SAME FAST on 1st and 5th gear
    but on 1st it is easy to wheelspin and on 5th very unlikely

    ALSO, car when driving at 1000 rpm of engine with torque 100 on wheels will accelerate two times slower than same car at 2000 rpm of engine (and double rpm of wheels) with same torque (100)
    (the power will be double)

    but don't even try to tell me that force on wheel is torque on wheel mutiplied by wheel speed
    why? because at 0 rpm (car & engine stopped) car would never be able to move as force would always be 0
    and electric engines are capable of generating torque at 0 rpm
  8. Oct 19, 2013 #7


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    Newton actually says...


    The force you refer to is not "acting on the body" being accelerated. In each case the force acting on the body is the same = 100N.
  9. Oct 19, 2013 #8


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    With an electric motor, torque decreases linearly as rpm increases. For the graph, torque = 3.2 (1 - rpm/600). As shown in the graph, power = torque x rpm x 2 x pi / 60. Power also equals force x speed, so force = power / speed = (torque x rpm x 2 x pi / 60) / v, where v is velocity. Assume bike's velocity is 2 m/s, then driven wheel force at 2 m/s versus rpm looks like:

    Code (Text):

      rpm  torque   power   force

        0   3.200   0.000   0.000
       50   2.933  15.359   7.679
      100   2.667  27.925  13.963
      150   2.400  37.699  18.850
      200   2.133  44.680  22.340
      250   1.867  48.869  24.435
      300   1.600  50.265  25.133
      350   1.333  48.869  24.435
      400   1.067  44.680  22.340
      450   0.800  37.699  18.850
      500   0.533  27.925  13.963
      550   0.267  15.359   7.679
      600   0.000   0.000   0.000
    Note that the maximum force occurs at the rpm corresponding to peak power. To optimize the gearing, you'd want the center point between shifts to be near the power peak. With a continously variable transmission, you'd want the motor rpm to be kept constant at 300 rpm regardless of the bikes speed.
    Last edited: Oct 19, 2013
  10. Oct 19, 2013 #9
    I agree that best power and ACCELERATION will be at 300 rpm.
    But you can't equal force with power.
    In your posted forces, at 0 rpm force is 0. So the car/bike would NEVER START MOVING. Which is not true.

    Also, look:
    imagine a sports car that has peak 400HP at 6000 rpm.
    I put first gear, accelerate slowly until i reach 5700 rpm at engine. Now i press acceleration pedal to the floor, what will happen? Rear (driven) wheels will start to spin.
    Now i put in 6th gear and accelerate so i have 5700 rpm. Which could be like 280km/h vehicle speed. At this moment i put acceleration pedal to the floor (actually for sure it was already at floor or near). What happens? NO WHEELSPIN, just acceleration.

    Why is that? because 5th gear provide times lower torque that in first gear. And force on wheel is: torque on wheel * wheel diameter.
    So the higher gear the force has to be lower.
    Look at this picture i posted earlier:
    those are torques and rotations of engine and wheel at each gear.

    Now look back at bicycle:

    The "engine" power is same in both bikes. Because of gearing, the bike on right is travelling 2 times faster that bike on left. But you see that force on wheel is different, and if you put both bikes on slippery surface, left one would wheelspin/crash when right one could still drive safely.
    We can see that bike on right is "applying" force over 2 times distance left bike, whatever "applying force" means. Newton say that force is a force, dosen't matter distance/speed its making.

    Wheel with axle is kind of machine with mechanical advantage https://en.wikipedia.org/wiki/Wheel_and_axle
    so gearing convert between more/less torque and more/less speed
    but what with acceleration? how to calculate it?
    Can't multiple torque * rotational speed because at 0rpm bike would never move. Also why does wheelspin not occur on sportscar in 6th gear at full power and occurs at 1st gear? the force has to be lower at 6th gear than 1, but acceleration force is same.
  11. Oct 19, 2013 #10


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    power = force x speed.
    force = power / speed.

    Note the assumption is that the bike is moving a 2 meters / second. This would require an infinitely tall gear to convert 0 rpm into 2 meters / second speed, so the driven wheel force would be zero.

    Assume the driven wheel has a radius of 1 meter, then here is the previous table showing the gear ratio corresponding to 2 meters / second.

    wheel rpm = motor rpm / gear
    wheel torque = motor torque * gear
    wheel force = wheel torque / (1 meter)

    Code (Text):

      rpm  torque   power   force    gear

        0   3.200   0.000   0.000   0.000
       50   2.933  15.359   7.679   2.618
      100   2.667  27.925  13.963   5.236
      150   2.400  37.699  18.850   7.854
      200   2.133  44.680  22.340  10.472
      250   1.867  48.869  24.435  13.090
      300   1.600  50.265  25.133  15.708
      350   1.333  48.869  24.435  18.326
      400   1.067  44.680  22.340  20.944
      450   0.800  37.699  18.850  23.562
      500   0.533  27.925  13.963  26.180
      550   0.267  15.359   7.679  28.798
      600   0.000   0.000   0.000  31.416
    Last edited: Oct 19, 2013
  12. Oct 19, 2013 #11
    But i don't want to have 0 rpm of engine at bike 2 m/s speed. I want to have my bike stopped and engine stopped. Now i apply eletrical power to engine so it starts generating torque at 0rpm. What force will be applied on wheels/on bike? Will it start to move? If i use your calculations the bike will never start.

    I understand that. And that means that the smaller gear will generate smaller torque and FORCE at wheels.
    now imagine i have engine attached to my car. and that engine is generating constant 50HP from 0 to 20000 rpm (that means torque is diminishing with revs).
    And i have gearbox taken from passanger car. I achieved my top speed of 100 km/h at full power on 3rd gear. NOW I CHANGE GEAR to 5 and apply full power. the power of engine is same, but the toque on wheel is smaller so is the force (!!). does that mean my car will start to decelerate to ~60-70km/h ?!! its not possible. power is a power. energy can't be lost.

    I don't understand what is the difference when i apply force 100N over 10 metres vs over 1 metre vs without movement. A force is a force. And acceleration is F/m.

    And how about my latest questions, about wheelspin?
    Last edited: Oct 19, 2013
  13. Oct 19, 2013 #12
    If you really achieve a top speed of only 100 km/h at full power in 3rd gear, then you will indeed find that if you switch to larger gear, that the car will slow down. (unless the engine was really far to the right on the downslope of the torque/rev curve, and the engine can produce much more torque in a higher gear).

    There will be no power disappearing, but the engine simply can't produce full power at the lower revs. There's only so much gasoline that can go in an explosion, and there's only so much explosions. (2 per revolution for a 4 cylinder car), and if there aren't enough explosions, the engine can't produce full power.

    EDIT: this goes for electric motors too, and even for human cyclists. There's a maximum torque that can be produced, so at low revs, you can't get the maximum power of the engine
    Last edited: Oct 19, 2013
  14. Oct 19, 2013 #13
    if you read my full post:

    this engine's power is constant 50HP no matter revolutions
  15. Oct 19, 2013 #14
    What you described in your last post was an engine that had to slow down in fifth, because it would produce less force in fifth than in 3rd gear. That's not compatible with constant power, no matter what the revolutions are. Such an engine is impossible anyway, because there's always a maximum torque, and therefore a minimum number of revolutions needed to get full power.
  16. Oct 19, 2013 #15
    The engine is electrical and its maximum torque is at 0 rpm, on bigger rpm it has lower torque so power remains constant. Full power is on any rpm on that engine.

    And seems we misunderstood. In my car i was driving full power at 3rd gear and switched to a fifth gear. Vehicle speed was same, speed of engine dropped but power remained the same.
    Then i asked a question, if on 5th gear power is same but force on wheel is lower, will the car slow down or keep the speed, if keep, why?
  17. Oct 19, 2013 #16


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    If the power is the same, and the speed is the same, the wheel force is the same. Power and wheel torque are not independent of each other.

    (That having been said, power is not constant for an electric motor - it hits its peak at about half the motor's maximum RPM, and falls off on either side of that value, which can be seen in your very first graph in this thread)
  18. Oct 19, 2013 #17


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    I really find it difficult to help people who act like they know more than centuries of science as opposed to people who want to try to understand where their understanding is flawed. If they are not looking for the flaws in their understanding they will continue to make the same mistaken assumptions over and over.

    I may be wrong, but I don't think you understand the relationship between torque and force, and how gearing changes the effective distances in converting torque to force. There also seems to be some misunderstanding of the nature/limitations of the power supplied through pedaling.

    Again, I may be misunderstanding your misunderstanding.

    Take a tiny wheel powered by a chain supplying torque. The torque is acting through a small distance, so the force is large (torque = force X distance, so force = torque/distance). That means rapid acceleration. If the wheel is large, the force is less for the same torque, so there is smaller acceleration. With the small wheel, if you could maintain the torque at all rotational speeds you would continue to accellerate at the same high rate forever.
  19. Oct 19, 2013 #18
    Really? then what if my car and engine is stopped. And now i apply electric power to motor. This motor can generate torque at 0 rpm. So there is also force on wheel. But the power is 0 because rpm is 0.
  20. Oct 19, 2013 #19


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    Look at the graph in the first post. The torque decreases linearly, and the power is at a maximum at 300 rpm, so the power versus rpm is not constant.
  21. Oct 19, 2013 #20
    Ok, but then how the car will start moving when its stalled and engine is stalled? if power is 0 at 0 rpm.
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