Power vs. Torque

In this article we are going to understand how the engine torque is produced, how engine power is calculated and what is a torque and power curve. Also, we are going to have a look at the engine torque and power maps (surfaces).

By the end of the article, the reader will be able to understand the difference between torque and power, how they affect the longitudinal dynamics of the vehicle and how to interpret torque and power curves at full load.

Definition of torque

Torque can be regarded as a turning force applied on an object. Torque (vector) is the cross product between a force (vector) and a distance (scalar). The distance, also called the lever arm, is measured between the force and the turning point. Similar to a force, torque is a vector and is defined by an amplitude and a direction of rotation.

Tightening torque at wheel bolt

Image: Tightening torque at wheel bolt

Imagine that you want to tighten/loosen the bolts of a wheel. Pushing or pulling the handle of the wrench connected to a nut or bolt, produces a torque (turning force) that loosens or tightens the nut or bolt.

The torque T [Nm] is the product of the force F [N] and the length of the lever arm a [m].

\[\bbox[#FFFF9D]{T = F \cdot a}\]

In order to increase the magnitude of the torque we can either increase the force, the length of the lever arm or both.

Example: Calculate the torque obtained on the bolt if the arm of the wrench has 0.25 m and the applied force is 100 N (which is approx. equivalent with a pushing force of 10 kg)

\[T = 100 \cdot 0.25 = 25 \text{ Nm}\]

The same torque could be obtained if the lever arm was 1 m and the force only 25 N.

The same principle applies to internal combustion engines. The torque at the crankshaft is produced by the force applied on the conrod journal through the connecting rod.

Torque at crankshaft

Image: Torque at crankshaft

The torque T will be produce at the crankshaft on each conrod journal, every time the piston is in the power stroke. The lever arm a in this case is the crank radius (offset).

The magnitude of the force F depends on the combustion pressure within the cylinder. The higher the pressure in the cylinder, the higher the force on the crankshaft, the higher the output torque.

Engine torque calculation function of cylinder pressure

Image: Engine torque calculation function of cylinder pressure

The length of the lever arm has impact on the overall engine balance. Increasing it too much can lead to engine imbalance, which results in higher forces in the crankshaft journals.

Example: Calculate the torque at the crankshaft for an engine with the following parameters:

Cylinder bore, B [mm]85
Cylinder pressure, p [bar]12
Crank offset, a [mm]62

First, we calculate the area of the piston (assuming the the piston head is flat and its diameter is equal with the bore of the cylinder):

\[A_p = \frac{\pi B^2}{4}=\frac{\pi \cdot 0.085^2}{4}=0.0056745 \text{ m}^2\]

Second, we’ll calculate the force applied to the piston. To get the force in N (Newton), we’ll use the pressure converted in Pa (Pascal).

\[F = p \cdot A_p = 120000 \cdot 0.0056745 = 680.94021 \text{ N}\]

Assuming that all the force in the piston goes into the connecting rod, the torque is calculated as:

\[T = F \cdot a = 680.94021 \cdot 0.062 = 42.218293 \text{ Nm}\]

The standard unit of measurement for torque is N·m (Newton meter). Especially in the USA, the unit of measurement for engine torque is lbf·ft (foot-pounds). The conversion between N·m and lbf·ft is:

\[ \begin{split}
1 \text{ lbf} \cdot \text{ft} &= 1.355818 \text{ N} \cdot \text{m}\\
1 \text{ N} \cdot \text{m} &= 0.7375621 \text{ lbf} \cdot \text{ft}
\end{split} \]

For our particular example, the torque in imperial units (USA) is:

\[T = 42.218293 \cdot 0.7375621 = 31.138615 \text{ lbf} \cdot \text{ft}\]

Torque T [N] can also be expressed as a function of the mean effective pressure of the engine.

\[T = \frac{p_{me} V_d}{2 \pi n_r}\]

where:
pme [Pa] – mean effective pressure
Vd [m3] – engine displacement (volume)
nr [-] – number of crankshaft rotations for a complete engine cycle (for a 4-stroke engine nr = 2)

Definition of power

In physics, power is the work done in time or, with other words, is the rate of doing work. In rotational systems, power P [W] is the product of the torque T [Nm] and angular velocity ω [rad/s].

\[\bbox[#FFFF9D]{P = T \cdot \omega}\]

The standard unit of measurement for power is W (Watt) and for rotational speed is rad/s (radian per second). Most of the vehicle manufacturers are providing the power of the engine in bhp (brake horse power) and the rotational speed in rpm (rotations per minute). Therefore, we are going to use conversion formulas for both rotational speed and power.

To convert from rpm to rad/s, we use:

\[\omega \text{ [rad/s]} = N \text{ [rpm]} \cdot \frac{\pi}{30}\]

To convert from rad/s to rpm, we use:

\[N \text{ [rpm]} = \omega \text{ [rad/s]} \cdot \frac{30}{\pi}\]

The engine power can also be measured in kW instead of W for a more compact value. To convert from kW to bhp and reverse, we use:

\[ \begin{split}
P \text{ [bhp]} &= 1.36 \cdot P \text{ [kW]}\\
P \text{ [kW]} &= \frac{P \text{ [bhp]}}{1.36}
\end{split} \]

In some cases you might find HP (Horse Power) instead of bhp as unit of measurement for power.

Having rotational speed measured in rpm and torque in Nm, the formula to calculate power is:

\[ \begin{split}
P \text{ [kW]} &= \frac{\pi \cdot N \text{ [rpm]} \cdot T \text{ [Nm]}}{30 \cdot 1000}\\
P \text{ [HP]} &= \frac{1.36 \cdot \pi \cdot N \text{ [rpm]} \cdot T \text{ [Nm]}}{30 \cdot 1000}
\end{split} \]

Example. Calculate the engine power in both kW and HP, if the engine torque is 150 Nm and engine speed is 2800 rpm.

\[ \begin{split}
P &= \frac{\pi \cdot 2800 \cdot 150}{30 \cdot 1000} = 44 \text{ kW}\\
P &= \frac{1.36 \cdot \pi \cdot 2800 \cdot 150}{30 \cdot 1000} = 59.8 \text{ HP}
\end{split} \]

Engine dynamometer

Engine speed is measured using a sensor on the crankshaft (flywheel). Ideally, to calculate power, we should also measure the torque at the crankshaft with a sensor. Technically, this is possible but not applied in the automotive industry. Because of the operating conditions of the crankshaft (temperatures, vibrations), measuring engine torque with a sensor is not a reliable technique. Also, the cost of a torque sensor is quite high. Therefore, engine torque is measured on the full range of speed and load, using a dynamometer (test bench), and mapped (stored) into the engine control unit.

Engine dynamometer schematic

Image: Engine dynamometer schematic

The dynamometer is basically a brake (mechanical, hydraulic or electrical) which absorbs the power produced by the engine. The most used and best type of dynamometer is the electric dynamometer. This is actually an electric machine that can be operated as a generator or motor. By varying the generator’s load torque, the engine can be put in any operating point (speed and torque). Also, with the engine at fuel cut (no fuel injection), the generator can be run as an electric motor to spin the engine. This way engine friction and pumping torque losses can be measured.

For an electric dynamometer, the rotor is connected to the crankshaft. The link between rotor and stator is electromagnetic. The stator is fixed through a lever arm to a load cell. To balance the rotor, the stator will push against the load cell. The torque T is calculated by multiplying the force F measured in the load cell with the length of the lever arm a.

\[T = F \cdot a\]

The engine parameters: brake torque, brake horse power (bhp) or brake specific fuel consumption (BSFC) contain the keyword “brake” because a dynamometer (brake) is used to measure them.

What comes out from a dynamometer engine test are torque maps (surfaces) which give the value of the engine torque at a specific engine speed and load (stationary operating points). The load of the engine is equivalent to the position of the accelerator pedal.

Example of torque map for a gasoline, spark ignition (SI) engine:

Engine
torque
[Nm]
Accelerator pedal position [%]
5102030405060100
Engine
speed
[rpm]
8004590107109110111114116
130060105132133134136138141
18003589133141142144145149
23001970133147148150151155
2800355133153159161163165
3300041126152161165167171
3800033116150160167170175
4300026110155169176180184
4800018106155174179185190
530001296147167175181187
58000484136161170175183
63000072120145153159171

Example of power map for a gasoline, spark ignition (SI) engine:

Engine
power
[HP]
Accelerator pedal position [%]
5102030405060100
Engine
speed
[rpm]
800510121213131313
13001119242525252626
1800923343636373738
2300623444848494951
2800122536163646566
3300019597176787880
3800018638187909295
43000166795103108110113
480001272106119122126130
53000972111126132137141
58000369112133140145151
63000065108130137143153

The electronic control module (ECM) of an ICE has the torque map stored in the memory. It calculates (interpolates) the engine torque function of the current engine speed and load. In the ECM, the load is expressed as intake manifold pressure for gasoline (spark ignition, SI) engines and injection time or fuel mass for diesel (compression ignition, CI) engines. The engine torque calculation strategy has corrections based on temperature and intake air pressure.

Plotting the torque and power data, function of engine speed and load, gives the following surfaces:

SI engine torque surface

Image: SI engine torque surface

SI engine power surface

Image: SI engine power surface

For a better interpretation of the torque and power maps, a 2-D torque line can be plotted for a fixed value of the accelerator pedal position.

SI engine torque curves

Image: SI engine torque curves

SI engine power curves

Image: SI engine power curves

Engine torque and power at full load

As you have seen, the torque and power of an internal combustion engine depend on both engine speed and load. Usually, engine manufacturers are publishing the torque and curve characteristics (curves) at full load (100% accelerator pedal position). Full load torque and power curves highlight the maximum torque and power distribution through the whole range of engine speed.

Engine torque and power parameters at full load

Image: Engine torque and power parameters at full load

The shape of the above torque and power curves are not from a real engine, the scope being to explain the main parameters. Nevertheless, the shapes are similar to the real characteristics of a spark ignited (gasoline), port injection, atmospheric engine.

Engine speed Ne [rpm] is characterized by four main points:

Nmin – is the minimum stable engine speed at full load
NTmax – is the engine speed at maximum engine torque
NPmax – is the engine speed at maximum engine power; also called rated engine speed
Nmax – is the maximum stable engine speed

At minimum speed, the engine should run smoothly, without oscillations or stalling. The engine should also allow operation at the maximum speed without any structural damage.

The full load engine torque curve Te [Nm] is characterized by four points:

T0 – engine torque at minimum engine speed
Tmax – maximum engine torque (peak torque or rated torque)
TP – engine torque at maximum engine power
TM – engine torque at maximum engine speed

Depending on the type of intake air (atmospheric or turbocharged) the peak torque can be either a point or a line. For turbocharged or supercharged engines, maximum torque can be kept constant between two engine speed values.

The full load engine power curve Pe [HP] is characterized by four points:

P0 – engine power at minimum engine speed
Pmax – maximum engine power (peak power or rated power)
PT – engine power at maximum engine torque
PM – engine power at maximum engine speed

The area between minimum engine speed Nmin and maximum torque engine speed NTmax is called low end torque zone. The higher the torque in this area, the better the launch/acceleration capabilities of the vehicle. When the engine is operating in this area, at full load, if the road resistance increase, the engine speed will decrease, which will result in a drop of engine torque and an engine stall. For this reason, this area is also called unstable torque region.

The area between maximum torque engine speed NTmax and maximum power engine speed NPmax is called the power band. During vehicle acceleration, for best performance, the gearshift (up) should be performed at maximum engine power. Depending on the gear ratios of the gearbox, after the gearshift, the selected gear will drop the engine speed at maximum torque, which will give optimum acceleration. Shifting the gears at maximum engine power will keep the engine speed within the power band.

The area between maximum power engine speed NPmax and maximum engine speed Nmax is called high end torque zone. Higher torque results in higher output power, which translates in higher maximum vehicle speed and better acceleration at high speed.

When the engine speed is kept between maximum torque engine speed NTmax and maximum engine speed Nmax, if the vehicle road resistance increases, the engine speed will drop and the output torque will increase, thus compensating for the road load increase. For this reason, this area is called the stable torque region.

Below you can find some full load torque and power curves examples for different types of engines. Notice the shape of the curves function of the type of the engine (spark ignited or compression ignited) and type of air intake (atmospheric or turbo(super)charged).

Honda 2.0 engine torque and power at full load

Cylinders architecture4 in-line

Honda 2.0 SI engine - torque and power curves at full load

Image: Honda 2.0 SI engine – torque and power curves at full load

Fuelgasoline (SI)
Engine capacity [cm3]1998
Fuel injectionvalve port
Air intakeatmospheric
Valve timingvariable
Tmax [Nm]190
NTmax [rpm]4500
Pmax [HP]155
NPmax [rpm]6000
Nmax [rpm]6800

Saab 2.0T engine torque and power at full load

Cylinders architecture4 in-line

Saab 2.0T SI engine - torque and power curves at full load

Image: Saab 2.0T SI engine – torque and power curves at full load

Fuelgasoline (SI)
Engine capacity [cm3]1998
Fuel injectionvalve port
Air intaketurbocharged
Valve timingfixed
Tmax [Nm]265
NTmax [rpm]2500
Pmax [HP]175
NPmax [rpm]5500
Nmax [rpm]6300

Audi 2.0 TFSI engine torque and power at full load

Cylinders architecture4 in-line

Audi 2.0 TFSI SI engine - torque and power curves at full load

Image: Audi 2.0 TFSI SI engine – torque and power curves at full load

Fuelgasoline (SI)
Engine capacity [cm3]1994
Fuel injectiondirect
Air intaketurbocharged
Valve timingfixed
Tmax [Nm]280
NTmax [rpm]1800 – 5000
Pmax [HP]200
NPmax [rpm]5100 – 6000
Nmax [rpm]6500

Toyota 2.0 D-4D engine torque and power at full load

Cylinders architecture4 in-line

Toyota 2.0 CI engine - torque and power curves at full load

Image: Toyota 2.0 CI engine – torque and power curves at full load

Fueldiesel (CI)
Engine capacity [cm3]1998
Fuel injectiondirect
Air intaketurbocharged
Valve timingfixed
Tmax [Nm]300
NTmax [rpm]2000 – 2800
Pmax [HP]126
NPmax [rpm]3600
Nmax [rpm]5200

Mercedes-Benz 1.8 Kompressor engine torque and power at full load

Cylinders architecture4 in-line

Mercedes Benz 1.8 Kompressor SI engine - torque and power curves at full load

Image: Mercedes Benz 1.8 Kompressor SI engine – torque and power curves at full load

Fuelgasoline
Engine capacity [cm3]1796
Fuel injectionvalve port
Air intakesupercharged
Valve timingfixed
Tmax [Nm]230
NTmax [rpm]2800 – 4600
Pmax [HP]156
NPmax [rpm]5200
Nmax [rpm]6250

BMW 3.0 TwinTurbo engine torque and power at full load

Cylinders architecture6 in-line

BMW 3.0 TwinTurbo SI engine - torque and power curves at full load

Image: BMW 3.0 TwinTurbo SI engine – torque and power curves at full load

Fuelgasoline
Engine capacity [cm3]2979
Fuel injectiondirect
Air intakedual-stage
turbocharged
Valve timingvariable
Tmax [Nm]400
NTmax [rpm]1300 – 5000
Pmax [HP]306
NPmax [rpm]5800
Nmax [rpm]7000

Mazda 2.6 rotary engine torque and power at full load

Cylinders architecture2 Wankel

Mazda 2.6 SI engine - torque and power curves at full load

Image: Mazda 2.6 SI engine – torque and power curves at full load

Fuelgasoline
Engine capacity [cm3]1308 (2616)
Fuel injectionvalve port
Air intakeatmospheric
Valve timingfixed
Tmax [Nm]211
NTmax [rpm]5500
Pmax [HP]231
NPmax [rpm]8200
Nmax [rpm]9500

Porsche 3.6 engine torque and power at full load

Cylinders architecture6 flat

Porsche 3.6 SI engine - torque and power curves at full load

Image: Porsche 3.6 SI engine – torque and power curves at full load

Fuelgasoline
Engine capacity [cm3]3600
Fuel injectionvalve port
Air intakeatmospheric
Valve timingvariable
Tmax [Nm]405
NTmax [rpm]5500
Pmax [HP]415
NPmax [rpm]7600
Nmax [rpm]8400

Key statements to keep in mind regarding engine power and torque:

Torque

  • torque is a component of power
  • torque can be increased by increasing the mean effective pressure of the engine or by lowering the torque losses (friction, pumping)
  • having a lower maximum torque distributed on a range of engine speeds its better from the traction point of view than having a higher maximum torque point
  • low end torque is very important for the launch capabilities of the vehicles
  • high torque is beneficial in off-road situation, when the vehicle is operated at high road gradients but low speed

Power

  • engine power depends on both torque and speed
  • power can be increased by increasing the torque or the engine speed
  • high power is important for high vehicle speeds, the higher the maximum power the higher the maximum speed of the vehicle
  • engine power distribution at full load, through the engine speed range, affects the acceleration capability of the vehicle at high speeds
  • for best acceleration performance, a vehicle should be operated in the power band, between maximum engine torque and power

For any questions or observations regarding this tutorial please use the comment form below.

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