# Power and speed relationship

### Power (physics) - Wikipedia

Power may be defined as the rate of doing work or the rate of using energy. These two definitions are equivalent since one unit of energy must be used to do one. One of the more difficult relationships to understand with regard to applications using electric motors is that between torque, power and speed. the frequently-misunderstood relationship between power and torque. is required to maintain the 10 GPM at 50 psi at operating speed.

## Power (physics)

The heavier you and your bike are, the more energy you must spend to overcome gravity. The combined weight of you the cyclist and your bike is W kg.

The gravitational force constant g is 9. The formula for gravitational force acting on a cyclist, in metric units, is: Friction between your tires and the road surface slows you down. The bumpier the road, the more friction you'll experience; the higher quality your tires and tube, the less friction you'll experience.

Power: Force and Velocity

As well, the heavier you and your bike are, the more friction you'll experience. There is a dimensionless parameter, called the coefficient of rolling resistance, or Crr, that captures the bumpiness of the road and the quality of your tires.

The formula for the rolling resistance acting on a cyclist, in metric units, is: As you cycle through the air, your bike and body need to push the air around you, similar to how a snowplow pushes snow out of the way.

### Power and Torque: Understanding the Relationship Between the Two, by EPI Inc.

Because of this, the air exerts a force against you as you ride. There are a few things that dictate how much force the air exerts against you. As well, you and your bike present a certain frontal area A m2 to the air. The larger this frontal area, the more air you have to displace, and the larger the force the air pushes against you.

### newtonian mechanics - Relationship between power and max. speed - Physics Stack Exchange

This is why cyclists and bike manufacturers try hard to minimize frontal area in an aerodynamic position. Finally, there are other effects, like the slipperyness of your clothing and the degree to which air flows laminarly rather than turbulently around you and your bike. Since, as explained above, 1 HP is 33, foot-pounds of work per minute, multiplying that number by 12 produces the number of inch-pounds of work per minute in one HPDividingby gives the units-conversion factor of Therefore, the simple equation is: When the equation is modified to include pump efficiency, it becomes: So suppose your all-aluminum V8 engine requires 10 GPM at 50 psi.

The oil pump will have been sized to maintain some preferred level of oil pressure at idle when the engine and oil are hot, so the pump will have far more capacity than is required to maintain the 10 GPM at 50 psi at operating speed. That's what the "relief" valve does: It is actually pumping roughly 50 GPM 10 of which goes through the engine, and the remaining 40 goes through the relief valve at 50 psi. The power to drive that pressure pump stage is: That pump at the same flow and pressure will consume: General Observations In order to design an engine for a particular application, it is helpful to plot out the optimal power curve for that specific application, then from that design information, determine the torque curve which is required to produce the desired power curve.

By evaluating the torque requirements against realistic BMEP values you can determine the reasonableness of the target power curve.

## - Power and Torque -

Typically, the torque peak will occur at a substantially lower RPM than the power peak. For a race engine, it is often beneficial within the boundary conditions of the application to operate the engine well beyond the power peak, in order to produce the maximum average power within a required RPM band.

However, for an engine which operates in a relatively narrow RPM band, such as an aircraft engine, it is generally a requirement that the engine produce maximum power at the maximum RPM. That requires the torque peak to be fairly close to the maximum RPM. For an aircraft engine, you typically design the torque curve to peak at the normal cruise setting and stay flat up to maximum RPM.

That positioning of the torque curve would allow the engine to produce significantly more power if it could operate at a higher RPM, but the goal is to optimize the performance within the operating range.

An example of that concept is shown Figure 3 below. The three dashed lines represent three different torque curves, each having exactly the same shape and torque values, but with the peak torque values located at different RPM values.

The solid lines show the power produced by the torque curves of the same color. Again, moving the same torque curve to the right another RPM blue, lb-ft torque peak at RPM causes the power to peak at about HP at RPM Using the black curves as an example, note that the engine produces HP at both and RPM, which means the engine can do the same amount of work per unit time power at as it can at The RPM band within which the engine produces its peak torque is limited.

You can tailor an engine to have a high peak torque with a very narrow band, or a lower peak torque value over a wider band. Those characteristics are usually dictated by the parameters of the application for which the engine is intended.

An example of that is shown in Figure 4 below. It is the same as the graph in Figure 3 aboveEXCEPT, the blue torque curve has been altered as shown by the green line so that it doesn't drop off as quickly.

Note how that causes the green power line to increase well beyond the torque peak. Alterations intended to broaden the torque peak will inevitable reduce the peak torque value, but the desirability of a given change is determined by the application.

Figure 4 Derivation of the Power Equation for anyone interested This part might not be of interest to most readers, but several people have asked: First, determine the distance it moves in one revolution: Now we know how far the crank moves in one revolution. How far does the crank move in one minute?