Torque Calculation with Total Load of 100 Kg

Torque Calculation with Total Load of 100 Kg

Hello, I have a bicycle with a total load of 100 kg. I need to calculate the starting torque necessary to propel the bicycle, taking into account either the wheel or the pedal (crank), and considering the rolling friction. Could you please provide a numerical explanation?

Answer:

To calculate the torque needed to start a bicycle, we first need to find the force needed to overcome the rolling resistance (rolling friction), and then apply it to the relevant distance (the radius of the wheel for wheel torque, or the length of the pedal crank for crank torque).

Let's start with calculating the force required to overcome rolling resistance:

Force due to rolling resistance:

Rolling resistance is a force that resists the motion of a body rolling on a surface. It is calculated by multiplying the rolling resistance coefficient (usually denoted by Crr) of the surface by the normal force (which is the weight of the bicycle plus the rider).

For simplicity, let's assume the coefficient of rolling resistance for a typical bicycle tire on asphalt is approximately 0.005. The weight (which is the mass times gravity) of the bicycle and the rider combined is 100 kg, and we'll take the acceleration due to gravity to be approximately 9.81 m/s².

Therefore, the rolling resistance force Frr would be:

Frr = Crr mass gravity

Frr = 0.005 100 kg 9.81 m/s²

Frr = 4.905 Newtons

Torque on the wheel:

Torque is the force applied to an object that causes it to rotate, and it's calculated by multiplying the force by the distance from the point of application of the force to the axis of rotation (in this case, the radius of the wheel).

Let's assume the wheel has a radius of 0.35 m (which is roughly the radius of a typical 700c road bike wheel).

The torque T on the wheel would then be:

T = Frr * r

T = 4.905 N * 0.35 m

T = 1.72 Nm

Torque on the pedal (crank):

To calculate the torque on the pedal (or crank), we have to consider the gear ratio as well, because the force exerted on the wheel is transmitted through the bicycle's gear system to the pedal.

The gear ratio is the ratio of the number of teeth on the chainring (front gears, connected to the pedals) to the number of teeth on the rear gear (connected to the wheel).

Let's assume a gear ratio of 3 (which would be reasonable for a bike on a flat surface). The force at the pedal is the force at the wheel divided by this gear ratio.

Let's also assume the length of the pedal crank is 0.17 m.

The force Fp at the pedal would be:

Fp = Frr / gear ratio

Fp = 4.905 N / 3

Fp = 1.635 N

The torque Tp at the pedal would then be:

Tp = Fp * crank length

Tp = 1.635 N * 0.17 m

Tp = 0.278 Nm

Which means, in this scenario, to start the bicycle, you would need to apply a torque of 1.72 Nm on the wheel or 0.278 Nm on the pedal.

Please note that these calculations are an oversimplification and many factors, such as air resistance, the efficiency of the bicycle's drive train, the slope of the road, and the starting inertia, have not been taken into account.

Replies

  • gohm
    gohm
    You are missing information. gear ratio? wheel diameter? length of crank arm? With your info you can only deduce the load is 50kg per wheel if two wheeled. You will take this 50kg weight at the drive wheel and multiply by the ratio of drive wheel size vrs. crank arm. Then multiply by the ratio of the front vrs. rear sprockets.
  • vvishwaskumar
    vvishwaskumar
    gohm
    You are missing information. gear ratio? wheel diameter? length of crank arm? With your info you can only deduce the load is 50kg per wheel if two wheeled. You will take this 50kg weight at the drive wheel and multiply by the ratio of drive wheel size vrs. crank arm. Then multiply by the ratio of the front vrs. rear sprockets.
    hello gohm..
    gear ratio = front sprocket/rear sprocket =2
    length of crank arm= 0.17 metres
    wheel radius= 0.33 metres
    so effort required = 50*2*(0.33\0.17) = 194.14 kg
    torque on pedal = 194.14*0.17*9.81 = 323.76 N-m
    is it possible to have this much of torque..?
    also a 150 cc bike is normally have 14 to 16 N-m torque, can it compare with bicycle calculation..? give me detailed explaination please
  • BigOhm
    BigOhm
    100 kg? Gohm, tell your little brother to quit riding on the handlebars?:roll:😁

    vvishwaskumar,

    There are a bunch of ways of looking at this, but one you might consider is just in terms of work. Think of the 100 kg bike. It's weight is 980 N and you might guess the rolling friction to be 0.05 with good tires and a good level surface. So, every meter the bike goes, you have 49 Nm of work. So work backwards and see how many radians your pedal crank has to go through to move the bike one meter. Throw in a 0.70 efficiency factor for the chain, bearings, etc etc. Then just set (Torque)(radians)(0.70) = 49 Nm.

    Sorry for not using math symbols. I'm a newbie and can't find them.
  • Rohan_sK
    Rohan_sK
    Gohm, dont you think that the Total Weight of the bike ie 100 kg must be considered while calcualting the Work done or hte Effort needed.

    The bike weighs 100 kg, so each wheel takes up 50 kg. But the force required to drive will be the total Inertia force ie 100 kg plus the frictional resistance ( here 0.05).

    So, Total Effort ( without the sporcket ratios, etc) = (W+f)9.81 = (100 + 0.05(100))(9.81). You can then multiply the sprocket wheels, crank arm ratios and get the Final Effort and Torque required.

    Correct me if I am wrong.
  • vvishwaskumar
    vvishwaskumar
    Rohan_sK
    Gohm, dont you think that the Total Weight of the bike ie 100 kg must be considered while calcualting the Work done or hte Effort needed.

    The bike weighs 100 kg, so each wheel takes up 50 kg. But the force required to drive will be the total Inertia force ie 100 kg plus the frictional resistance ( here 0.05).

    So, Total Effort ( without the sporcket ratios, etc) = (W+f)9.81 = (100 + 0.05(100))(9.81). You can then multiply the sprocket wheels, crank arm ratios and get the Final Effort and Torque required.

    Correct me if I am wrong.
    thanks rohan, but how this much torque is possible..think and
    also a 150 cc bike is normally have 14 to 16 N-m torque, can it compare with bicycle calculation..? 100kg=bicycle weight(15kg) + rider weight(85kg)
  • vvishwaskumar
    vvishwaskumar
    hey guys help me for calculation......please
  • rpower
    rpower
    give the coefficient of friction.
    You want to calculate starting torque that means the torque to overcome static friction bw wheel and ground.
    static friction(forcew) = u(coeff of friction) x N (weight normal reaction)
    torque at wheels=forcew x radius of wheel.
    divide this by 2(gear ratio)
    u'll get the torque applied by rider to accelerate the bike from 0.
  • vvishwaskumar
    vvishwaskumar
    😁
    rpower
    give the coefficient of friction.
    You want to calculate starting torque that means the torque to overcome static friction bw wheel and ground.
    static friction(forcew) = u(coeff of friction) x N (weight normal reaction)
    torque at wheels=forcew x radius of wheel.
    divide this by 2(gear ratio)
    u'll get the torque applied by rider to accelerate the bike from 0.
    thanx rpower...
    i am getting from this .torque on pedal = 8 Nm and effort applied on pedal=5 kg..and it looks feasible because 150cc bike normally have 15 Nm of torque.
    also can we compare the bicycle torque with that of bike..in terms of their mechanics....? reply please
  • rpower
    rpower
    vvishwaskumar
    😁

    thanx rpower...
    i am getting from this .torque on pedal = 8 Nm and effort applied on pedal=5 kg..and it looks feasible because 150cc bike normally have 15 Nm of torque.
    also can we compare the bicycle torque with that of bike..in terms of their mechanics....? reply please
    I do not understand your question compare torque of bicycle with motorbike "in terms of mechanics" !!😒
  • vvishwaskumar
    vvishwaskumar
    rpower
    I do not understand your question compare torque of bicycle with motorbike "in terms of mechanics" !!😒
    a 150 cc bike is normally have 14 to 16 N-m torque, can it compare with bicycycle torque...?
    also we are using a chain drive for transmitting torque from wheel to pedal...so is there no any consideration for tension on sides and moment of inertia....?
  • rpower
    rpower
    in a bike or car there are several inertial loses. innertial loses in transmission , then in differential (in cars), in running engine components.
    e.g Torque(clutch)=torque(engine)- Ia
    where I is moment of inertia of engine cmponents and a angular acceleration
  • vvishwaskumar
    vvishwaskumar
    rpower
    I do not understand your question compare torque of bicycle with motorbike "in terms of mechanics" !!😒

    sorry


    but in calculating torque do u not think that, as the power is transmitted by chain drive from front to rear sprocket, there is also a consideration of tension in the chain...?
  • rpower
    rpower
    Ofcourse, tensions on tight side (upper) and slack side (down) of the chain drive are to be taken into account.

    [T(tight) - T(slack)] velocity = Power
  • gohm
    gohm
    As far as the weight issue, it totally depends on if you are only condsidering torque at the drive wheel. Energy loss would be used in the calculation to equate a procise calculation however this problem does not appear to need to factor that based on the info provided by the OP. Sounds like a class theory problem.
  • sachin121
    sachin121
    hi have vehical of four wheels having 150mm dimeter. i need to transport load of 50kg with velocity 3m/s then which motor should i select .please send me motor specification
  • sophia9rev
    sophia9rev
    some great tip guys..#-Link-Snipped-# ....my dads a mechanical engineering but heslearning to use the forums
  • beyonbala
    beyonbala
    vvishwaskumar
    😁

    thanx rpower...
    i am getting from this .torque on pedal = 8 Nm and effort applied on pedal=5 kg..and it looks feasible because 150cc bike normally have 15 Nm of torque.
    also can we compare the bicycle torque with that of bike..in terms of their mechanics....? reply please
    I don't understand how did u arrive at 15Nm ..
    Also when searched for static friction co efficient between wheel and tyre, it is found to be 0.7-0.8.
    what is that 0.05?
  • techfresh
    techfresh
    with out specifying the force you are applying at the pedal/crank how can you calculate the torque ??? the weight is acting over the bicycle not on the pedal ,please be specific about your question

    #-Link-Snipped-#
  • Dev92
    Dev92
    Hey fellas, i am working on a project where in which i have brought a few changes to pulsar 150 bike, my end result is increase in rpm which we have achived, now help me out about how to calculate the torque for the same??? plz reply
  • wanderer2711
    wanderer2711
    will the torque applied be reduced/increased when we use a shaft drive instead of a chain drive ?
  • wanderer2711
    wanderer2711
    will the torque applied be reduced/increased when we use a shaft drive instead of a chain drive ?
  • Deepak Durgasrinivas
    Deepak Durgasrinivas
    Generally what is cycle weight which was commonly using in India and how much force is applying on pedal
  • ImSj17
    ImSj17
    I am designing a electric bicycle... Load applied is 120 Kg so how can I calculate torque if I use 600 watt motor

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