# Calculating Wheel Torque to Accelerate Up a Hill

• les3002
In summary, to design a vehicle that can accelerate up a 1/8 gradient hill to 11.11m/s in 15 seconds, the effort required would be 357N. To find the torque at the wheel, the effort needs to be multiplied by the wheel radius. This should be taken into consideration when choosing an appropriate motor and gear ratio for the vehicle. Torque is the turning effect of a force and is measured in Newtons meter.
les3002
i have to design a vehicle that will accelerate up a 1/8 gradient hill to 11.11m/s in 15s

i need the effort required and wheel torque.

mass = 170kg
rolling resistance = 50N/t (0.05N/kg)
air resistance = 13.6N
g = 9.81m/s^2

i have calculated:

a = 11.11*(1/15) = 0.74m/s^2
theta = 7.18 deg
sin theta = 0.125 deg

so i have the effort as:

E = ma+mgsin_theta+Froll+Fair
E = 125.8+(170*9.81*0.125)+0.05+13.6
E = 347.9125N

is E the torque i need at the wheels?
if not how would you go about working it out.

i tried with a motor of 40N, wheel radius of 0.2m and gear ratio of 10:1

i worked it out like this.
axle torque = 40*10 = 400N

so to find the torque at the wheel do i divide the axle torque by wheel radius

400/0.2 = 2000 that seems wrong to me??

You need to multiply the rolling resistance with the mass:

$$E = m(a + R + g/8) + 13.6 = 357\ N$$

which makes only a slight difference.

To find the torque at the wheel, $$\Gamma _w$$, you need to multiply the effort by your wheel radius. The effort will be shared by the four wheels (if all four a driving) reducing the torque to a quarter at each wheel.

In order to choose an appropiate motor you need to consider the torque of the motor,$$\Gamma _m$$, and gear ratio $$G$$ such that

$$\Gamma _m \times G = \Gamma _w$$,

http://www.blueink.com/CLASS/physcom1/gear.htm"

Torque, $$\Gamma$$, is the turning effect of a force $$F$$. If the force is applied with a longer lever arm $$r$$ the turning effect will be greater:

$$\Gamma = F \times r$$

the S.I. units of torque is Newtons meter.

Last edited by a moderator:

I would approach this problem by first breaking down the forces acting on the vehicle. The main force required to accelerate the vehicle up the hill is the force of gravity, which is dependent on the mass of the vehicle and the slope of the hill. In this case, the force of gravity is 170kg*9.81m/s^2*sin(7.18 degrees) = 125.8N.

Next, we need to consider the forces that oppose the motion of the vehicle, such as rolling resistance and air resistance. Rolling resistance is dependent on the weight of the vehicle, so we can calculate it by multiplying the weight (170kg*9.81m/s^2) by the rolling resistance coefficient (0.05N/kg). This gives us a rolling resistance force of 85.5N. Air resistance is a bit more complex, as it is dependent on the speed of the vehicle and the aerodynamic properties of the vehicle.

To calculate the effort required, we can use the equation E = ma + mg*sin(theta) + Froll + Fair, where m is the mass of the vehicle, a is the acceleration, g is the acceleration due to gravity, theta is the slope of the hill, Froll is the rolling resistance force, and Fair is the air resistance force. Plugging in the values given in the problem, we get E = 170kg*0.74m/s^2 + 125.8N + 85.5N + 13.6N = 347.9N. This is the total effort required to accelerate the vehicle up the hill.

To calculate the wheel torque, we need to take into account the gear ratio and the wheel radius. The gear ratio tells us how much the motor torque is multiplied before it reaches the wheels. In this case, with a gear ratio of 10:1, the torque at the wheels will be 10 times larger than the motor torque. We also need to consider the wheel radius, as torque is equal to force multiplied by radius. So, to calculate the torque at the wheels, we divide the total effort required by the gear ratio and the wheel radius. In this case, it would be 347.9N/(10*0.2m) = 1739.5N*m.

It is important to note that this calculation assumes that the motor is able to provide a constant torque throughout the acceleration

## 1. How do I calculate wheel torque to accelerate up a hill?

To calculate wheel torque, you need to know the weight of the vehicle, the slope of the hill, and the acceleration desired. You can use the formula: Torque = (Vehicle weight x Slope x Acceleration) / Number of Drive Wheels. This will give you the total torque required to accelerate up the hill.

## 2. What is the role of wheel torque in accelerating up a hill?

Wheel torque is the force that is responsible for moving the vehicle up the hill. It is the rotational force produced by the wheels that allows the vehicle to overcome the force of gravity and accelerate up the slope.

## 3. How do I determine the weight of the vehicle for calculating wheel torque?

The weight of the vehicle can be determined by using a scale or by referring to the manufacturer's specifications. It is important to use the weight of the vehicle and not the weight of the cargo, as the vehicle's weight is what needs to be overcome when accelerating up a hill.

## 4. Is wheel torque the same for all types of vehicles?

No, wheel torque can vary depending on the size and weight of the vehicle, as well as the type of drivetrain it has. For example, a larger and heavier vehicle will require more torque to accelerate up a hill compared to a smaller and lighter vehicle.

## 5. Can wheel torque be increased to improve performance when accelerating up a hill?

Yes, wheel torque can be increased by adding a more powerful engine, using a lower gear ratio, or by using specialized systems such as a turbocharger or supercharger. However, it is important to consider the limitations of the vehicle and its components when making such modifications.

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