Here is a interesting article about HP and Torque. It was written by "Tox" in Atlas F1 Forum as a reply to my thread. Unfortunately I do not know his real name so I can not give to him proper credits.

"Some people say horsepower is how long you can
continue to make torque. That's sorta true, but it's "long" in terms of higher rpms,
not time directly. Think of it in this old fashioned way. Put a pulley on the crankshaft
of the engine with a 1 ft radius (2 ft diameter). Attach a long rope to that pulley.
Dangle it over a 6283 ft cliff, (I chose that distance because the pulley diameter is 2 ft
and the circumference is 6.283 ft and I want to move it for one minute at 1000 revolutions
per minute.) add a 200 lb weight to the end.
If the engine can develop 200 ft-lbs of torque it can lift that 200 lb weight directly.
If it does it at only 1000 rpms then it takes 1 minute to lift 200 lbs, 6283 ft up. (incidentally
for those wonder where the acceleration is.. It's gravity acting on the weight at 1G)
But let's say it can't rev any faster than 1000 rpms (like a big cruise boat diesel engine),
then the max hp is only 200 ft-lbs * 1000 rpms / 5252 = 38hp. Pitiful.

We don't want to wait a full minute, so we need to lift the weight faster.
So now we use an engine that can make 200 ft-lbs of torque but at 2000 rpms, it
can lift that same 200 ft-lbs weight twice as fast, pulling it 6283 ft up the cliff in
only 30 seconds. max HP = 200 ft-lbs * 2000 rpms / 5252 = 76 hp.

Ok.. So let's give this engine some serious guts, better breathing, higher revving,
larger displacement. Rev it all the way up to 5252rpms, and get it to still
make 200 ft-lbs of torque (no mean feat). Now it takes only 11.4 seconds to lift a
200 lb weight up a 6283 ft cliff. And of course HP = 200 ft-lbs * 5252 rpms / 5252 = 200 hp.

There's the basics of hp versus torque as measured at the crank for any
given fixed rpm. When the concept of horsepower was dreamed up,
these are the sorts of applications the steam engines it applied to, were used for. Lifting big
weights, pulling things through or over the ground, or turning the entire contents of some
factory at a constant rpm.

So what happens when a Honda engine manages to make 150 hp but
only 100 ft-lbs of torque at 8000 rpms? (I didn't choose VTEC numbers because I want round numbers)
Well.. For one it simply won't be able to lift the 200 lb weight with a crank pulley that has a
1 ft radius. It can't. It's only generating 100 ft-lbs of lifting force.
What you need now is gears. Let's put a 2 to 1 gearset between the engine crank and rope
pulley. Now the engine is still turning at 8000 rpms, but the pulley is turning at 4000 rpms, and
we've effectively doubled its leverage so torque measured at the pulley is 200 ft-lbs again.
Torque at pulley = 200 ft-lbs @ 4000 rpms. So it now can actually lift the 200 lb
weight directly, and at 4000 rpms, thats 4 times faster than our original engine. So 15 seconds
to lift the 200 lb weight up 6283 ft. Not bad. Moving a 200 lb weight up over 1 vertical
mile in only 15 seconds. (Note, 100 ft-lbs * 8000 / 5252 = 200 ft-lbs * 4000 / 5252)

One interesting side note. It's possible for an engine or motor to make torque at 0 rpms.
A steam train engine, for instance has a direct drive from pistons to wheels so when it
needs to get moving it can actually generate some ungodly number like 10000 ft-lbs of
torque at 0 rpms and thus by our formula HP = 1000 ft-lbs * 0 / 5252 = 0 hp. Cute eh?
Electric motors also can do this. That's why diesel train engines drive use electric motors
to turn the wheels, and a big nearly constant rpm engine to power the generator that
powers the motors.

Summary so far.
So torque lifts the weight. We can convert low engine torque (Honda engine)
into high usable torque through gearing, but at the cost of speed.
Horspower tells you how fast the weight can be lifted at a constant angular velocity.

Ok.. In the next post I'll explain how this relates to acceleration.

Horsepower, Torque and how you use it to accelerate through gearing
So what's the whole deal with the "torque curve" and why's it important to acceleration?
Well.. only being able to make good torque at a single rpm is not very useful for a road going vehicle.
It's ok for a train engine driving a generator, or factory motor, but no sense for a car. If you
only make useful torque at the crank in a very narrow range of rpms then you need lots and
lots of gears to keep the torque at the wheels in a useable range as your vehicle's speed
increases. Maximum acceleration of a car is made possible by maximizing your output
torque at the wheels at ALL times. Let's say the torque curve for our original engine that
made 200 ft-lbs of torque at 1000 rpms can actually do it between 500 and 1000 rpms (absolutely
flat curve) and falls off sharply on either side. (below 500 and above 1000).
It can still accellerate, but it'd need maybe a 2:1 gear to get started, then 1:1 to
keep going, and then about 2 overdrive gears to go fast. like 1:2.. 1:4
So here's our gears. 1st: 2:1 2nd: 1:1 3rd: 1:2 4th: 1:4
In first gear at the output wheesl, it'd make 400 ft-lbs of torque to the ground between
250-500 rpms. Second gear.. 200 ft-lbs at 500 to 1000 rpms.. 3rd.. 100 ft-lbs at 1000 to 2000 rpms
4th 50 ft-lbs between 2000 to 4000 rpms.. This engine makes 200 ft-lbs * 1000 / 5252 = 38hp.

By the time you hit the top of 4th gear you're only putting 50 ft-lbs of torque to the ground, but
you're moving right along. If you only had to lift only a 50 lb-weight up our cliff you could get there
in 15 seconds (not counting acceleration though the gears).

Works the other way around too. A higher revving engine that makes a little torque
up high. Let's try a flat torque curve between 2000 and 4000 rpms of only 100
ft-lbs. Let's try to match the torque to the ground of our other engine with
gearing. 1st: 4:1 2nd: 2:1 3rd: 1:1 4th: 1:2
So at the ground. 1st gear makes 400 ft-lbs of torque between 500 and 1000 rpms
2nd: 200 ft-lbs between 1000 and 2000 rpms
3rd: 100 ft-lbs between 2000 and 4000 rpms..
and 4th: 50 ft-lbs between 4000 and 8000 rpms.

Oops.. I accidentally made a more powerful engine. I was making the same
torque to the ground at the top of 3rd gear and still have 50 ft-lbs
usable for the next 4000 rpms in 4th. Want to see something cute.
At the crank. 100 ft-lbs * 4000 rpms / 5252 = 76 hp.
At the wheels.. 50ft-lbs * 8000 rpms / 5252 = 76 hp..
(assuming zero drivetrain loss here). You see why it doesn't
matter if you make your dyno pull in 3rd or 4th gear?

So yes. Torque is what does the actual work. With our weight, any
output torque less than 200 ft-lbs will NOT lift it at all. But horsepower
is how FAST we we do the work. And acceleration depends on the engine's
ability to generate torque at more than just one rpm. The fatter
the torque curve is (no matter how small the max torque value), the faster
you can accelerate because the more rpms you have to work with, the
higher the gear ratios and thus the higher your torque at the ground.
You maximize torque to the ground through gearing keeping the engine in the rpm
range where the engine generates the most ground speed for a given torque value.

A car that only generates 50 ft-lbs of torque, but but can do it between 10,0000 and 20,000
rpms will still make 190 hp. You're saying "But Ian, I still need raw TORQUE to accelerate
right?" True. But the tires don't need to turn at 20,000 rpms, so there's where I'm going to
get my torque. Let's design a single gear. The tires only need to turn at 880 rpms to go 60mph at
the top of 2nd gear. So let's experiment with an effective gear ratio from crank to tires
of 20:1. That'd give me 50 * 20 = 1000 ft-lbs of torque at the ground between the engine
rpms of 10k and 20k. That'd certainly get you moving just fine. Does it
work speedwise? 10,000 rpms / 20 = 500.. 20,000 rpms / 20 = 1000.
with 205/50-15 tires that's a speed range of 34mph to 68mph.
Cool.. An engine that generates only 50ft-lbs of torque between 10k and 20k rpms
manages to put down 1000 ft-lbs of torque to the ground between 34mph and 68mph
in my imaginary 2nd gear. Now just design another half dozen gears and you're
good to go. And it'll *feel* like 1000 ft-lbs of torque the entire time too.

An old turbo formula 1 car that makes 1100 hp at 14 thousand rpms.. Lesee.. 412 ft-lbs of
torque up there in the stratospheric rpms. Whew. Try a 10:1 effective gearing, that's still
like 4000 ft-lbs of torque to the ground at 95mph. Not bad.

So yes, you *feel* torque, but it's torque at the ground, not at the engine. If you can
rev high enough, then gearing will increase your effective torque to the ground for
a longer period of time. Torque you feel.. torque applied for a large range of rpms
equates to faster acceleration, and the highest rpm that you can maintain useful
torque will be your peak horsepower number. The horsepower @ rpm value
gives you some idea of how long the torque curve extends into the rpms.
That's how you use it.

So there it is. Everything you never needed to know about torque and horsepower.

__________________
Tox!"