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# Relationship between power and torque6

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## Relationship between power and torque

(OP)
From basic physics we know, that:
P = M * w/t, where:
P - power
m - torque
w - angle of rotation
t - time

This can be translated into this formula:
P = M * n / 9550, where:
n - RPM

In other words, a power is directly proportional to torque. Then how does the dyno tests of car engines produces curves, where P and M are not directly proportional?

Thank you for explanation

### RE: Relationship between power and torque

If you take (torque(w) * w) you should get power(w). Where w is a chosen RPM.

### RE: Relationship between power and torque

Because an internal combustion engine does not produce a linear torque curve, the curves do not appear to be directly proportional- but they are.

If you take a dyno plot from an engine and look at individual RPM points, the values will fit the equation 100% of the time.

If you look at a dyno plot where the units are ft-lb and HP, if the torque and power curves are plotted on the same x and y scale, they will cross at 5252 every single time- because the equation to calculate power from torque and speed in those units is (Torque x RPM) / 5252.

Power is a function of torque and speed, not a quantity that we directly measure. Torque and speed are always measured, and power is always calculated. You cannot directly measure power.

### RE: Relationship between power and torque

I don't understand your question? You want to know how it does it or why the formula still works?

You formula comment "In other words, a power is directly proportional to torque" is simply wrong. Power and torque are only directly proportional if you hold rpm constant. Similarly, power and rpm are only directly proportional if you hold torque constant. If you don't understand this then Google directly proportional.

The formula has both torque and rpm. When both can vary the power is never directly proportional to either value. The torque an engine can produce varies with the rpm and the engine rpm is never a constant in a vehicle drive train so both are always changing. It doesn't matter though, because the formula still applies even if both RPM and torque are changing.

### RE: Relationship between power and torque

2
Power is directly proportional to the product of torque and RPM. Most dynos used in engine development laboratories (directly connected to the engine, not those speed shop dynos driven by the wheels) measure engine speed and torque, the power curve is computed from that data.

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### RE: Relationship between power and torque

another point on the wheel dynos - I've seen at least one magazine article comparing output power with different tires installed, where the tires had different diameter. They concluded that the power curve had been changed significantly, but what had really changed was the relationship between dyno roller RPM and engine RPM.

### RE: Relationship between power and torque

If the RPM ratio changes, power must also change- power is a function of RPM.

Going to a bigger tire decreases torque at the contact patch, making the apparent load on the engine higher- which has exactly the same effect on vehicle performance as reducing engine power. Everything is a function of torque and speed- so if you change one of those you change everything.

### RE: Relationship between power and torque

I think that answer is missing a bit of detail. Changing tire diameter doesn't have exactly the same effect as reducing engine power - it has an effect similar to changing transmission or differential ratio. Assuming all your tests are done in the lowest gear, you might conclude that vehicle acceleration is affected in the same way as it would be if engine power was lower over a significant portion of the operating range, but even in that scenario you would see the curves cross at the right hand side of the graph (which is not the same as simply increasing or reducing power as w/throttle restriction).

In the case of the article I'm referring to, I think they concluded that lower-profile tires had less frictional losses than standard-profile tires and therefor increased power at the wheels by 5% or so ... but they had missed the shift in the curve caused by tire diameter and virtually the entire effect they "measured" could be explained by that factor alone.

### RE: Relationship between power and torque

(OP)
Thank you everybody, who participated in this discussion, for helping me understand this topic. Now I get it, and I appreciate your help!

### RE: Relationship between power and torque

ivymike, something else to keep in mind when reading popular magazine articles about dyno testing are the unmentioned factors that drive variability. Speed shops are pretty far from using lab grade equipment much less having air-handling systems capable of feeding constant temp, constant humidity air to the engine which over a few hours can easily affect power 3-5% by itself. Add in a vehicular cooling system, driveline, and all the lil games operators play and you've got significant variability run-run in the vehicle. Taken a step further, many shops use a simple inertia dyno and measure power and torque at a moment in time vs a continuous load.

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