Jmac279
Horsepower = Torque (lb-ft)*RPM/5252
So if you have 300 hp from say 4000 RPM to 8000 RPM, torque at 4000 RPM would be ...
300 = Torque (lb-ft) *4000/5252
300*5252/4000 = 393.9 lb-ft
At 8000 RPM, torque would be down to ...
300 = Torque (lb-ft) * 8000/5252
300*5252/8000 = 196.95 lb-ft
So Torque has dropped by half, but Horsepower remains the same ...
Now, to get to your question... A higher-revving engine would allow a higher gear ratio to achieve the same speed, which translates into more force ...
Force (lbs) = Wheel Torque (lb-ft) * Gear Ratio * Final Drive Ratio * 24 / Tire Diamater (outer, in)
MPH = RPM * Diameter (outer, in) / (Gear Ratio * Final Drive Ratio * 336)
At 60 MPH at 4000 RPM with a 2 foot diameter tire and a 4.0 final drive ratio ...
60 = 4000*24/(GR*4*336)
GR = 4000*24/(24*4*336)
GR = 1.190
At 60 MPH at 8000 RPM with a 2 foot diameter tire and a 4.0 final drive ratio ...
GR = 8000*24/(60*4*336)
GR = 2.381
As you can see, the gear ratio has doubled and, therefore, Force will be be the same (196.95 * 2 = 393.9 *1) ...
So Force would be equal at those RPMs with their respective gear ratios, but AVERAGE Force would be greater with the higher-revving engine ...
At 4000 RPM with the 1.190 gear ratio, Force would be ...
Force (lbs) = 393.9*1.19*4*24/24
Force = 1874.964 lbs
At 4000 RPM with the 2.381 gear ratio, Force would be ...
Force (lbs) = 393.9*2.381*4*24/24
Force = 3751.5036 lbs
So Force will have doubled at 4000 RPM and will be equal at 8000 RPM, meaning a much greater Force (1.5x more average Force to be exact) than the PEAK force of the engine shifted at 4000 RPM ...
And, since Acceleration = Force/Mass, 1.5x more Force = 1.5x greater acceleration
To expand a little...
The whole object of racing is to maximize the amount of torque to the wheels for the maximum amount of time. This is done with gears. Gears are torque multipliers. They give a motor a mechanical advantage. Imagine gears working like this: You are trying to turn a ratchet. Your hand is all the way by the socket. Even by using your maximum force, the bolt won't turn. Now move your hand to the end of the handle. By using less than your maximum force the bolt will turn.
Torque is the amount of twisting force the motor can apply to the crankshaft and horsepower is the amount of work the motor can perform over time (rpm).
The torque at wheels of the car or truck is what gets the vehicle moving. The torque at the engine crankshaft is multiplied (increased) to the wheels by an amount equal to the gear ratio in the transmission. Thus, the torque at the wheels of the car is much higher than the torque generated at the engine crankshaft. For example, take a gear ratio that is 8.55:1 in first gear, the torque being delivered to the wheels is equal to this number multiplied
by the engine torque at whatever RPM you're at. It's actually a little lower than that because energy is lost through the transmission, commonly refered to as mechanical or parasitic loss, however, you get the point.
Suppose the engine RPM is 5600 RPM, then the maximum speed the car can go in first gear is equal to 5600 divided by 8.55 (the gear ratio), which equals 655 RPM, or 50 mph. This 655 RPM is how fast the wheels are rotating, and based on the size of the tire, this translates into a forward speed of 50 mph for the car. And from 0-50 mph, the torque being generated at the wheels of the car is equal to gear ratio (8.55) multiplied by the engine torque. As you go up in gear, the gear ratio decreases so that the torque delivered to the wheels is less.
Now again, for racing or acceleration, you want to maximize the amount of torque at the wheels for the longest period of time. Without going into a lengthy explanation, you achieve this by using an engine that makes alot of torque at high RPM, i.e, horsepower according to the famous equation relating torque to horsepower. mentioned above. Since these values cross at 5252 rpms, torque will be higher than horsepower below that number and horsepower will be higher than torque above that number. Ever wonder why old muscle cars have higher torque ratings vs horsepower ratings? Bingo- low redlines. But of course peak numbers don't tell the whole story.
Having an engine that makes alot of torque at high RPM (i.e, hp) means that you can do either:
(1) Have high gear ratios in your transmission, which means the torque delivered to the wheels is high because the transmission is increasing the engine torque by a large factor (for example., 15:1 in 1st gear in a honda S2000), or
(2) Stay in the lower gears at higher speeds since your redline is very high. Since the gear ratios are higher in the lower gears, the torque at the wheels will be higher as well, and thus, you accelerate quicker.
Trucks are not designed to go fast at high speeds, nor are they designed to accelerate quickly. They must, however, move a large amount of mass from a standstill, and thus have engines that make alot of engine torque at low RPM's. However, because of the fact that they make low horsepower and have a low redline, the torque generated at the wheels of the truck decreases rapidly as their speed increases. That's okay though, it's a truck. It's not meant to "let's go from a roll".
At the other extreme, F1 and Indy Cart racing cars have very high horsepower (~800 hp) and low engine torque (~250 ft-lbs). However, because these engines
generate their engine torque at high RPM's (~14,000 RPM), they can use high gear ratios so that the torque generated at the wheels is VERY high.
Conversely, they can use low gear ratios, which means they can stay in the lower gears at much higher speeds. Either way, the torque being delivered
the the wheels of the car from 0-150 mph is much higher than if they had an engine that made 250 hp and 800 ft-lbs.
Ok, I'm done blabbing.
BTW - Good post jmac