Wheel torque can be calculated function of engine torque if the parameters and status of the transmission are known. In this tutorial, we are going to calculate the wheel torque and force for a given:
- engine torque
- gear ratio (of the engaged gear)
- final drive ratio (at the differential)
- (free static) wheel radius
Also, we are going to assume that there is no slip in the clutch or torque converter, the engine being mechanically linked to the wheels.
This method can be applied to any powertrain architecture (front-wheel drive or rear-wheel drive) but, for an easier understanding of the components, we are going to use a read-wheel drive (RWD) powertrain.
Image: Vehicle rear-wheel drive (RWD) powertrain diagram
As depicted in the image above, the engine is the source of torque. The gearbox is connected to the engine through the clutch (on a manual transmissions) or torque converter (on an automatic transmissions). We consider that there is absolutely no slip in the clutch (fully closed) or in the torque converter (lock-up clutch closed). In this case the engine torque Te [Nm] is equal with the clutch/torque converter torque Tc [Nm].
\[T_c = T_e \tag{1}\]
Further, the engine torque is transmitted through the gearbox, where is multiplied with the gear ratio of the engaged gear ix [-] and outputs the gearbox torque Tg [Nm].
\[T_g = i_x \cdot T_e \tag{2}\]
The propeller shaft is transmitting the torque to the rear axle, where is multiplied with the final drive gear ratio i0 [-]. This gives the torque at the differential Td [Nm].
\[T_d = i_0 \cdot T_g \tag{3}\]
If the vehicle is driven on a straight line, the torque at the differential is equally split between the left wheel Tlw [Nm] and the right wheel Trw [Nm].
\[T_{lw} = T_{rw} = \frac{T_d}{2} \tag{4}\]
Image: Vehicle rear-wheel drive (RWD) powertrain schematic
The sum of the left and right wheel torque gives the torque at the differential.
\[T_{lw} + T_{rw} =T_d \tag{5}\]
Replacing (2) in (3) in (4) gives the mathematical expression of the wheel torque function of the engine torque, for a given gearbox ratio ix and a final drive ratio i0.
\[\bbox[#FFFF9D]{T_w = \frac{i_x \cdot i_0 \cdot T_e}{2} }\tag{6}\]
If we consider nw [-] as the number of driving wheels, then the wheel torque formula will have the general form of:
\[\bbox[#FFFF9D]{T_w = \frac{i_x \cdot i_0 \cdot T_e}{n_{w}} }\tag{6.1}\]
If the vehicle is rear wheel drive (RWD) or front wheel drive (FWD) then nw = 2, if the vehicle is four wheel drive (4WD) or all wheel drive (AWD) the nw = 4. If the vehicle is a motorcycle then nw = 1.
The formula of the wheel torque (6) applies to a vehicle which is driven on a straight line, where the left wheel torque is equal with the right wheel torque.
\[T_{lw} = T_{rw} = T_w \tag{7}\]
From mechanics (static), we know that the torque is the product between a force and its lever arm length. In our case, the wheel torque is applied in the wheel hub (center) and the lever arm is the wheel radius rw [m]. For this example we assume that both wheel have the same radius rw.
\[T_{lw} = F_{lw} \cdot r_w \tag{8}\]
The same principle applies to the right wheel torque.
\[T_{rw} = F_{rw} \cdot r_w \tag{9}\]
Assuming that both left and right wheel torque and radius are equal, we can write a generic expression of the wheel force Fw [N], function of wheel torque Tw [Nm] and wheel radius rw [m].
\[T_{w} = F_{w} \cdot r_w \tag{10}\]
From (10) we can extract the formula of the wheel force function of the wheel torque and wheel radius.
\[\bbox[#FFFF9D]{F_{w} = \frac{T_w}{r_w}} \tag{11}\]
Replacing (6) in (10) will give the mathematical expression of the wheel force function of engine torque, gearbox gear ratio, final drive ratio and wheel radius.
\[\bbox[#FFFF9D]{F_{w} = \frac{i_x \cdot i_0 \cdot T_e}{2 \cdot r_w}} \tag{12}\]
For a different number of driving wheels nw [-], the general formula for wheel force becomes:
\[\bbox[#FFFF9D]{F_{w} = \frac{i_x \cdot i_0 \cdot T_e}{n_{w} \cdot r_w}} \tag{12.1}\]
Example 1. Calculate the wheel torque and force for a rear wheel drive vehicle (RWD) with the following parameters:
- engine torque, Te = 150 Nm
- gearbox (1st) gear ratio, ix = 4.171
- final drive ratio, i0 = 3.460
- tire size marking 225/55R17
Step 1. Calculate the (free static) wheel radius from the tire size marking. The method for calculating the wheel radius is described in the article How to calculate wheel radius. The calculated wheel radius is rw = 0.33965 m.
Step 2. Calculate the wheel torque using equation (6).
\[T_w = \frac{i_x \cdot i_0 \cdot T_e}{2} = \frac{4.171 \cdot 3.460 \cdot 150}{2} = 1082.3745 \text{ Nm}\]
Step 3. Calculate the wheel force using equation (11).
\[F_{w} = \frac{T_w}{r_w} = \frac{1082.3745}{0.33965} = 3186.7349 \text{ N} \]
Example 2. For a given gearbox, with multiple gears (gear ratios), we can calculate the wheel torque and force for each gear. Let’s calculate the wheel torque and force for a vehicle with the following parameters:
- engine torque, Te = 150 Nm
- wheel radius, rw = 0.33965 m
The gearbox is automatic (ZF6HP26), with the following gear ratios and final drive ratio.
| Gear # | Gear ratio symbol | Gear ratio |
| 1 | i1 | 4.171 |
| 2 | i2 | 2.340 |
| 3 | i3 | 1.521 |
| 4 | i4 | 1.143 |
| 5 | i5 | 0.867 |
| 6 | i6 | 0.691 |
| Final drive | i0 | 3.460 |
To speed up calculations, we can use a Scilab script.
clc// Input dataTe = 150;ix = [4.171 2.340 1.521 1.143 0.867 0.691];i0 = 3.460;rw = 0.33965;nw = 2;// Wheel torque and force calculationTw = (ix .* i0 .* Te)/nw;Fw = Tw ./ rw;// Display resultsmprintf("\n%s\t\t%s\t\t%s\t\t%s\n","Gear","ix [-]","Tw [Nm]","Fw [N]")for i=1:length(ix) mprintf("%d\t\t%.3f\t\t%.2f\t\t%.2f\n",i,ix(i),Tw(i),Fw(i));end Executing the above script will output the following results in the Scilab console:
Gearix [-]Tw [Nm]Fw [N]14.1711082.373186.7322.340607.231787.8131.521394.701162.0841.143296.61873.2850.867224.99662.4160.691179.31527.94
Example 3. For our third example we are going to use the full load torque curve of an engine and calculate the wheel torque and force (traction) in each gear. Calculate the wheel torque and force (traction) for a vehicle with the following parameters:
- engine torque, Te = 150 Nm
- wheel radius, rw = 0.33965 m
- the gear ratios of ZF6HP26 (see Example 2)
The engine torque at full load is given by the following parameters:
| Ne [rpm] | 800 | 1312 | 1800 | 2276 | 2800 | 3316 | 3806 | 4300 | 4770 | 5300 | 5800 | 6300 |
| Te [Nm] | 116 | 135 | 148 | 157 | 165 | 172 | 178 | 184 | 188 | 187 | 183 | 171 |
where Ne is engine speed and Te is engine torque.
The graphical representation of the engine speed and torque points is depicted in the image below.
Image: Engine torque at full load function of engine speed
Since we need to perform a lot of calculations, we’ll use a Scilab script to calculate the wheel torque and force curves for each gear. The results are going to be plotted in a graphical window.
clc// Input dataNe = [800 1312 1800 2276 2800 3316 3806 4300 4770 5300 5800 6300];Te = [116 135 148 157 165 172 178 184 188 187 183 171];ix = [4.171 2.340 1.521 1.143 0.867 0.691];i0 = 3.460;rw = 0.33965;nw = 2;// Plot engine torquefigure(1)hf = gcf();hf.background = 8;plot(Ne,Te,"LineWidth",2)xgrid()xlabel("Engine speed [rpm]","FontSize",3)ylabel("Engine torque [Nm]","FontSize",3)title("x-engineer.org","Color","blue","FontSize",2)// Calculate wheel torque and forcefor i = 1:length(ix) for j = 1:length(Te) Tw(i,j) = (ix(i) .* i0 .* Te(j))/nw; Fw(i,j) = Tw(i,j) ./ rw; endend// Plot wheel torque and forcefigure(2)hf = gcf();hf.background = 8;plot(Ne,Tw,"LineWidth",2)xgrid()xlabel("Engine speed [rpm]","FontSize",3)ylabel("Wheel torque [Nm]","FontSize",3)title("x-engineer.org","Color","blue","FontSize",2)legend("1st gear","2nd gear","3rd gear","4th gear","5th gear","6th gear",2)figure(3)hf = gcf();hf.background = 8;plot(Ne,Fw,"LineWidth",2)xgrid()xlabel("Engine speed [rpm]","FontSize",3)ylabel("Wheel force [N]","FontSize",3)title("x-engineer.org","Color","blue","FontSize",2)legend("1st gear","2nd gear","3rd gear","4th gear","5th gear","6th gear",2) Executing the script will output the following graphical windows.
Image: Wheel torque at full load function of engine speed and gear
Image: Wheel force at full load function of engine speed and gear
The same method can be applied for an electric vehicle, the engine torque being replaced by the motor torque.
You can also check your results using the calculator below.
Wheel torque calculator
| Te [Nm] | ix [-] | i0 [-] | rw [m] | nw [-] |
| Tw [Nm] = | ||||
| Fw [N] = | ||||
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FAQs
How do you calculate wheel torque? ›
To calculate the torque seen at the wheel, divide the engine torque by the drive train loss ratio.
What is the formula to calculate torque? ›How is torque calculated? τ = F ⋅ r \tau = F\cdot r τ=F⋅rtau, equals, F, dot, r. The direction of the torque vector is found by convention using the right hand grip rule.
How do you calculate torque needed to rotate a wheel PDF? ›To calculate load torque, multiply the force (F) by the distance away from the rotational axis, which is the radius of the pulley (r). If the mass of the load (blue box) is 20 Newtons, and the radius of the pulley is 5 cm away, then the required torque for the application is 20 N x 0.05 m = 1 Nm.
How is torque calculated in cars? ›The formula for figuring out torque is torque = horsepower of the engine x 5252, which is then divided by the RPMs. The problem with torque, however, is that it is measured in two different places: directly from the engine and to the drive wheels.
What is the formula for a wheel? ›Use the formula: c = 2_pi_r, where c is the circumference, r is the radius, and pi can be approximated by 3.14. Following the example, if the car wheel has a radius of 0.3 meters, then the circumference is equal to: 0.3 x 3.14 x 2 = 1.89 meters.
How do you calculate power to wheels? ›Now, write power as torque T (Newtons) times angular velocity w (radians per second) where RPM is wheel RPM. P = 2 pi T RPM/60 = mav. That's it. The wheel RPM is directly proportional to velocity, so once you know torque, mass and velocity, you can calculate acceleration.
Why do we calculate torque? ›When studying how objects rotate, it quickly becomes necessary to figure out how a given force results in a change in the rotational motion. The tendency of a force to cause or change rotational motion is called torque, and it's one of the most important concepts to understand in resolving rotational motion situations.
How do you solve torque problems? ›How to Solve Torque Problems Easily - YouTube
How do you calculate torque with hand rule? ›The Right Hand Rule for Torque - YouTube
How do you calculate torque in torsion? ›The equivalent torque can be found with: where n[rad/s] = N[rev/min]×2π/60. Similar to the moments of inertia that you learned before in rotational kinetics and bending of beams, the polar moment of inertia represents a resistance to twisting deformation in the shaft.
How do you calculate flywheel torque? ›
- Where Tfw is the Flywheel Torque (N-m)
- m is the flywheel mass (kg)
- r is the radius (m)
- a is the angular acceleration (rad/s^2)
In this experiment a flywheel is so mounted that torques can be applied to it by hanging a mass M from the free end of a string, the remainder of which is wrapped around the axle. The torque due to the weight is τ = Tr where T is the tension in the string and r the radius of the axle.
What is torque in engine or car? ›Torque is a twisting force that speaks to the engine's rotational force and measures how much of that twisting force is available when an engine exerts itself. Torque is present in everyday happenings, such as operating a doorknob, opening a soda bottle, using a wrench, or pedaling a bicycle.
What is the formula for wheel and axle? ›In the case of a wheel and axle, the ideal mechanical advantage can be calculated using the equation IMA=Rr I M A = R r where R is the radius of the wheel and r is the radius of the axle.
How do you calculate wheel HP? ›The equation to calculate horsepower is simple: Horsepower = Torque x RPM / 5,252.
How is wheel size calculated? ›Wheel Diameter
Wheel or rim diameter is the distance measured in inches across the face of the wheel, from bead seat to bead seat. It's measured this way because that's where the tire and the wheel come together. In our example, the diameter is 16 inches.
Broadly, 15 per cent of the engine's peak power is lost to friction, getting to to the wheels from the crank. So 300 kilowatts/horsepower (whatever) at the crank is about 250 at the wheels (ballpark estimate). But manufacturers all measure power at the crank.
How much torque does a 1 HP motor have? ›The 3600 RPM, 1HP motor produces 1.5 ft. lbs. of torque at 3600 RPM. So if your 1HP pump was operating at 1800 RPM, the 1800 RPM motor would be producing 3 ft.
How do you calculate engine force? ›The force (thrust) is equal to the exit mass flow rate times the exit velocity minus the free stream mass flow rate times the free stream velocity.
What are the 3 factors that determine torque? ›Examples: Page 5 Torque is Determined by Three Factors: The magnitude of the applied force. The direction of the applied force. The location of the applied force.
What is the unit of torque? ›
The SI unit for torque is the Newton-metre or kgm2sec-2. How have we come to this? If we look at the formula Torque = Force X Distance. While distance is measured in metres and force is measured in newton, so torque is measured in newton ⋅ metres.
Does torque change with speed? ›Since the rated output power of a motor is a fixed value, speed and torque are inversely related. As output speed increases, the available output torque decreases proportionately.
What is torque formula and examples? ›Solved Example on Torque Formula
The distance from the bolt to the mechanic's hand is 0.40 m. Find out the magnitude of the torque applied? Answer: The angle between the moment the arm of the wrench and the force is without a doubt 90°, and sin 90° θ = 1. The torque is: T = F × r × sinθ
Ch 15 Torque Fundamentals (5 of 13) How to Calculate a ... - YouTube
How do you calculate torque in fluid mechanics? ›Physics - Mechanics: Fluid Statics (1 of 1) Calculating the Torque on a ...
Is torsion equal to torque? ›Torque and torsion are both related to turning effects experienced by a body. The main difference between torque and torsion is that torque describes something that is capable of producing an angular acceleration, whereas torsion describes the twist formed in a body due to a torque.
What is the formula of torsion constant? ›From its definition, we see that the torsion constant may be obtained by plotting a graph of torque vs. angular displacement and calculating the slope. Κ = I 2Tπ . The STATIC METHOD and DYNAMIC METHOD can be performed in either order, but you must use the same rod in both parts of the experiment.
What is the formula for torsional stiffness? ›where I p = π D 4/32 is the polar moment of inertia of a circular cross section. Thus, the torque required for unit twist, i.e., T (θ) is called the torsional stiffness.
What is flywheel formula? ›Moment of inertia of a flywheel is calculated using the given formula; I = N m N + n ( 2 g h ω 2 − r 2 )
What is the torque for flywheel bolts? ›Tighten all bolts evenly, ¼ turn at a time in a crisscross pattern until flywheel is completely drawn-up to the crankshaft. Torque all bolts in 3 steps: First to 25 ft/lbs. then 60 ft/lbs. Final torque to: 78 - 80 ft/lbs.
How do you measure a flywheel? ›
Using a dial caliper, measure from the flywheel friction surface to the straight-edge. Record the distance. Again, using the dial caliper, measure from the engine housing flange to the straight-edge. Subtract this distance from the previously recorded distance.
What is the formula for rotating? ›...
Rotation Formula:
| Rotation | Point coordinate | Point coordinate after Rotation |
|---|---|---|
| Rotation of 90^{0} (Anti-Clockwise) | (x, y) | (-y, x) |
| Rotation of 180^{0} (Both) | (x, y) | (-x, -y) |
| Rotation of 270^{0} (Clockwise) | (x, y) | (-y, x) |
| Rotation of 270^{0} (Anti-Clockwise) | (x, y) | (y, -x) |
Ch 15 Torque Fundamentals (2 of 13) Direction of Torque (Part 1) - YouTube
How do you calculate net torque in physics? ›Physics, Net Torque (5 of 13) Five Forces Applied to a Door - YouTube
What's the difference between torque and torque? ›Horsepower vs Torque - A Simple Explanation - YouTube
What is engine torque used for? ›Applied to internal combustion engines or electric motors, torque indicates the force to which the drive shaft is subjected. Torque is expressed in pound-feet (lb-ft) or newton-meters (Nm). The interaction of torque and engine speed (rpm) determines the engine power.
How do you calculate torque from horsepower? ›- Torque (lb.in) = 63,025 x Power (HP) / Speed (RPM)
- Power (HP) = Torque (lb.in) x Speed (RPM) / 63,025.
- Torque (N.m) = 9.5488 x Power (kW) / Speed (RPM)
- Power (kW) = Torque (N.m) x Speed (RPM) / 9.5488.
Solved Example on Torque Formula
The distance from the bolt to the mechanic's hand is 0.40 m. Find out the magnitude of the torque applied? Answer: The angle between the moment the arm of the wrench and the force is without a doubt 90°, and sin 90° θ = 1. The torque is: T = F × r × sinθ
If F is force and r is radius, then torque =F ×r.
What is the formula of torque in magnetic field? ›τ = N I A B sinθ
This is the torque on a current-carrying loop in a uniform magnetic field. This equation can be shown to be valid for a loop of any shape. The loop carries a current I, has N turns, each of area A and the perpendicular to the loop makes an angle θ with the field B. The net force on the loop is zero.
How do you calculate torque in KG? ›
Torque is measured in Newton meters and is calculated by N·m = (kg*m²)/s².
How do you calculate torque and torque? ›Measure the distance, r , between the pivot point and the point the force is applied. Determine the angle θ between the direction of the applied force and the vector between the point the force is applied to the pivot point. Multiply r by F and sin θ and you will get the torque.
What are the 3 units of torque? ›Torque Units: SI, Metric and American
There are three common torque units: SI (International Standard) based on Newton meters, Metric based on kilogram force centimeters, and American/ English based on inch pounds.
In order to ensure proper operation of indicating instruments, the following three torques are required: Deflecting torque. Controlling torque. Damping torque.
What is torque equal to? ›By definition, torque τ = r × F. Therefore, torque on a particle is equal to the first derivative of its angular momentum with respect to time.
What does R stand for in torque? ›Equation. Symbol breakdown. Meaning in words. τ = r F sin θ = r ⊥ F \tau = rF\sin\theta = r_\perp F τ=rFsinθ=r⊥F. τ \tau τ is torque, F is applied force, r is the radius from the axis of rotation to the location where the force is exerted, and θ is the angle between F and r when these vectors are placed tail to tail.
What is torque example? ›Torque is the expression of a rotational or twisting force. The engines in vehicles rotate about an axis, thus creating torque. It can be viewed as the strength of a vehicle. Torque is what rockets a sports car from 0-60 kmph in seconds.
What is universal torque equation? ›The universal torque equation is obtained when all the elements are considered in the relay i.e., T = T1 + T2 + T3 + T4. Substituting equations of T1, T2, T3, and T4 in the above equation, we get, T = K1 I2 + K2 V2 + K3 V I cos(θ - 𝜏) + K4. The above equation represents the universal torque equation of relay.
How do you calculate torque in a circular coil? ›Calculating the Torque on a Current Carrying Coil in a Magnetic Field
What is the formula for the torque on a current loop? ›Torque on the loop can be found using τ=NIABsinθ τ = N I A B sin θ . Maximum torque occurs when θ=90∘ θ = 90 ∘ and sinθ=1 sin θ = 1 .