Why does the torque & power curve always cross at the same point?

It's a mathematical quirk arising from the relationship between torque and power and it's only true for the same set of units which also makes it entirely irrelevent to engine performance.

The commonly used formula is HP equals torque in ft-lb x rpm divided by 5,252, in which case the lines will cross at 5,252 rpm.

However if the units of torque are changed to in-lb the formula becomes HP equals torque x rpm divided by 63,025 and the lines will cross at 63,025 rpm.

Since, by definition, power equals force by distance the quirk comes about because of the conversion from force to torque, the latter being the force acting at the radius of a circle... 1 foot in the first formula, 1 inch in the second.

The mathematics is somewhat complicated as it involves reducing the formula to its basic units and cancelling out the common factors. There are fully worked examples online if you want to pursue it futher.

Thanks for explaining one is just a mathematical construct of the other. Why do they even bother if one is just a mathematical twist of the other?

Why not just have one curve?

This may help:

They both show the same thing, but they show it in different ways and it's more convenient to look at one than the other depending on what you're wanting to calculate.

--scott

Because it matters not where the lines cross as the power curve is calculated directly from the torque curve based on actual dynamometer readings (since power can't be measured directly).

The most relevant points on those curves are the peaks and rpm at which they occur since they serve to indicate an engine's power band (the rev range over which it performs most efficiently). This might help....

Also relevant might be the tendency of sales folk (and others) to quote maximum torque in isolation of rpm as if it were a performance indicator when it really means jack shit since flywheel torque isn't what appears at the drive wheels (unless it's a Tesla). :)

Thank you for your help and advice.

I think the simplest answer was the one that explained torque is measured and horsepower is simply calculated from that torque measurement using the number 5,252 because of units.

If different units are used, the crossover point in RPM will be different.