Except that doesn't apply to tractors

.

It applies perfectly to tractors. Yes, the formula/time thing was just a typo/brain fart, I fixed it, thanks for pointing it out.

As for the rest, yes, HP is a calculation, which is what I said. You only measure torque under load and convert it. HP is typically measured at the engine crank, and the torque multiplication happens after that. So the engine output is separate from what you end up with in your final drive, which is up to the transmission and axles (or PTO gears).

You ever notice how a torque curve is usually pretty flat but the HP curve starts low, climbs and then drops off?

This is a HP and torque curve for an International DT466:

Note that the torque output is almost constant through most of the RPM range, except very low idle and towards the end when the engine can no longer keep up.

If you check JD engine specs for a 2032R (gen 2), you will see that its max HP is 30.7 at 2500 RPM. At this RPM, the rated engine speed, it produces 64.2 lb ft of torque.

But...its maximum torque is 77.4 lb ft, and that is produced at 1625 RPM.

What that tells you, based on what I said in my original comment, is that this engine produces a certain amount of torque, which increases slightly as the RPMs go up and then starts to taper off as the revs continue to climb. At some point, you reach the point at which the engine produces the most power, which is not always or usually the most torque. In fact, as evidenced by the 2032R (and 38R and I think most or even all other tractors), the torque the engine produces actually drops off after a certain RMP, but the power continues to climb (e.g. 2032R, torque tops out at 1625 RPM, then drops steadily until 2500 RPM, past which point it drops off rapidly). So even though the engine is making less torque at higher RPMs, it is producing more HP because it is applying that torque

**faster** (higher RPM). That's how you get HP, which is work over time.

Or to put it another way...

What happens when you measure is that the dyno applies a load (resistance) that the engine has to overcome. Then you increase RPMs. The result is the torque curve, which represents the maximum torque produced at every point throughout the rev range. At some point, that torque curve takes a dive because the engine doesn't have enough power to apply torque much beyond this speed. So what you have with the torque curve is a measure of the engine's ability to overcome resistance (do work) at various RPMs. Since RPMs are a measure of how fast that work is being done, that gets converted into horsepower with the above mentioned formula.

That's it. It's that simple. AFTER that, you can apply gearing (transmission) to change the final output torque at the wheels and the PTO.

Let's look at the PTO. Let's pretend for a moment that there is no parasitic loss from the hydro. With the engine spinning at its rated RPM (say the 2032R at 2500 RPM), the PTO spins at 540 RPM (or thereabouts). The engine is spinning 4.6 times faster than the PTO. This means that the PTO gearing reduces speed and amplifies torque. So you take 64.2 ft lbs of torque at 2500 RPM and reduce that to 540, which gives you almost 300 ft lbs @ 540 RPM at the PTO, which, when we run it through the formula, gives us

**the same HP** as 64 ft lbs at 2500 RPM. Now we know PTOs don't work that way, that there is a lot of loss in the hydro, but it should serve to explain how the torque amplification works. If there were no parasitic loss from the hydro at all (which is impossible) that is what you would see at the PTO.

Hope that makes sense.