Horsepower v torque
There is a lot of confusion about the relationship between horsepower and torque, I was guilty until I decided to do some investigating. Here is my summary. Lets cut to the chase, in the context of this article it is torque and torque alone that accelerates a car. That's great you think, my big block sticks out 750lbfft of torque and that small high revving engine only puts out 250lbfft, I'll blow him away. Sadly its not quite as straight forward as that, there is a small caveat I did not mention, what I should of said was it's torque at the wheel and torque at the wheel alone that accelerates a car. All things being equal the car that has the most torque at the wheel will be accelerating harder. Well your first reaction may be 750lbfft is 3 times 250 so there is no contest, wrong. It's all about gearing, the best way to explain is an example, see diagram below.

OK, we have two engines both putting out 714hp, one makes 750lbfft at the engine and the other 250lbfft. The important factor is the speed at which the torque is made. The small engine is revving 3 times faster, so we can gear it down with a 3:1 ratio to achieve the same rpm at the output shaft (the wheels in real life). The consequences of this is the torque is multiplied 3 times, hey presto we have the same torque at the output shaft.
So after having said that torque alone accelerates a car, the torque figure is meaning less if we don't know at what rpm the torque is being made, this is where horsepower come in. Think of horsepower as a way of factoring in rpm to the torque equation.
You may be surprised, I know I was, but horsepower is simply a calculation based on rpm and torque. Dynos and rolling roads only ever measure torque. Horsepower is calculated after. Here's the formula:
Horsepower = Torque * RPM / 5252
So how is this formula arrived at, and where did 'horsepower' come from?
Well it's all down to the Scottish engineer James Watt (1736 to 1819), he established that a horse could pull a 550lb weight up from a coal mine at a rate of one foot every second, for an eight hour shift. This converts to 33,000 foot pounds per minute. He published these observations, stating this figure to be the equivalent of one horsepower.
We need to convert from the rotary motion of an engine to a linear motion, like the horse example. Remember we can only measure the torque of the engine, this is expressed in pound feet. A pound foot of torque is the twisting force necessary to support a one pound weight on a weightless horizontal bar, one foot from the centre of rotation. Lets rotate the one pound weight one revolution, the distance travel is 6.2832, that's Pi multiplied by the diameter, 2 feet. We have now done 6.2832 foot pound of work.
One horsepower equals 33,000 foot pounds per minute, so if we divide 6.2832 in to
33,000 we can conclude that we at 5252 rpm we are producing one horsepower, we are
moving our one pound weight 33,000 feet every minute.
Therefore if we multiply the torque by rpm and then divide by 5252 we can calculate
the horsepower.
Lets see what we now know:
 A car will be accelerating hardest in any given gear when at its peak torque
 Horsepower is a calculation based on torque.
 Torque means nothing without knowing what rpm it occurs at.
 Horsepower factors rpm in to the torque equation.
 It's better to make torque at high rpm rather than low rpm, so we can take advantage of gearing.
So which is king?
Lets look at a constant rpm example, a really interesting one is a constantly variable
transmission, CVT. These transmissions vary the gear ratio on the fly and effectively
have an infinite number of gears. Do you think we should keep the engine at peak
torque or peak horsepower for maximum acceleration?
From my previous statement: A car will be accelerating hardest in any given gear when at its peak torque, it's got to be peak torque, WRONG. Lets do some calculations to prove why.
Engine Rpm  Engine Torque  Engine hp  Variable Gear Ratio  Torque at Wheel  Target Wheel rpm 
1800  53  18  4.50  238.50  400 
2100  123  49  5.25  645.75  400 
2400  184  84  6.00  1104.00  400 
2700  268  138  6.75  1809.00  400 
3000  291  166  7.50  2182.50  400 
3300  306  192  8.25  2524.50  400 
3900  333  247  9.75  3246.75  400 
4200  349  279  10.50  3664.50  400 
4800  346  316  12.00  4152.00  400 
5100  344  334  12.75  4386.00  400 
5400  341  351  13.50  4603.50  400 
5700  339  368  14.25  4830.75  400 
6000  325  371  15.00  4875.00  400 
6300  306  367  15.75  4819.50  400 
In the above tabulation, you can see typical torque and horsepower values, the column on the right is a chosen nominal wheel speed, it could have been any speed, as long as it's constant. The idea is to see where peak torque at the wheels occurs, in other words the point at maximum acceleration. The Gear ratio column is Engine rpm divided by the Target wheel rpm. The Torque at wheel column is Gear ratio multiplied by Engine torque.
Let's look down the Torque at wheel column to find the highest value: 4875, move to the left and you will see that we are at peak horsepower!
Oh boy this is getting really confusing, does this then mean there must be a point when accelerating through the gears that maximum acceleration occurs at peak horsepower and not peak torque?
No, acceleration still occurs at peak torque. This is because we are in a fixed gear situation. We are using the increase in engine rpm to move the car forward. The CVT uses constant rpm and changes the gear ratio to move the car forward.
Lets add a few more columns to the chart just to clarify things a bit more.
Constantly variable transmission  Fixed gear transmission  
Engine Rpm  Engine Torque  Engine hp  Variable Gear Ratio  Torque at Wheel  Target Wheel rpm  Fixed Gear Ratio  Torque at Wheel  Wheel Speed 
1800  53  18  4.50  238.50  400  15  795  120 
2100  123  49  5.25  645.75  400  15  1845  140 
2400  184  84  6.00  1104.00  400  15  2760  160 
2700  268  138  6.75  1809.00  400  15  4020  180 
3000  291  166  7.50  2182.50  400  15  4365  200 
3300  306  192  8.25  2524.50  400  15  4590  220 
3900  333  247  9.75  3246.75  400  15  4995  260 
4200  349  279  10.50  3664.50  400  15  5235  280 
4800  346  316  12.00  4152.00  400  15  5190  320 
5100  344  334  12.75  4386.00  400  15  5160  340 
5400  341  351  13.50  4603.50  400  15  5115  360 
5700  339  368  14.25  4830.75  400  15  5085  380 
6000  325  371  15.00  4875.00  400  15  4875  400 
6300  306  367  15.75  4819.50  400  15  4590  420 
In the Fixed gear ratio column there is a value of 15, this is the ratio at which
we made the most torque at the wheel with the CVT. The wheel speed is obviously
changing but at 6000 rpm the CVT and fixed gear data match. Where does maximum acceleration
occur? At maximum torque, but of course at a different wheel speed.
The fixed gear system makes 5235 lbfft torque at 280 wheel speed, out of interest lets see what torque would be made with a CVT:
Constantly variable transmission  
Engine Rpm  Engine Torque  Engine hp  Variable Gear Ratio  Torque at Wheel  Target Wheel rpm 
1800  53  18  6.43  340.71  280 
2100  123  49  7.50  922.50  280 
2400  184  84  8.57  1577.14  280 
2700  268  138  9.64  2584.29  280 
3000  291  166  10.71  3117.86  280 
3300  306  192  11.79  3606.43  280 
3900  333  247  13.93  4638.21  280 
4200  349  279  15.00  5235.00  280 
4800  346  316  17.14  5931.43  280 
5100  344  334  18.21  6265.71  280 
5400  341  351  19.29  6576.43  280 
5700  339  368  20.36  6901.07  280 
6000  325  371  21.43  6964.29  280 
6300  306  367  22.50  6885.00  280 
6964 lbfft, the sooner they perfect this technology the better!
Well I've got side tracked a little, back to question in hand 'which is king'
Torque or Horsepower? Well the question is in fact a nonstarter, as stated, torque
means absolutely nothing without rpm, so you cannot compare the two.
It's like saying which is faster 100miles or 100mph! Dumb question hey?
An excellent analogy I've seen on the web is the Waterwheel that produces 2600 lbfft
of torque, that's impressive, if we connected the water wheel up the wheels of a
car then we could shoot up to 60mph in a flash, without the Waterwheel noticing.
Wrong! Back to gearing again, the ratio required to spin the wheels at 60mph would
leave us with 43 lbfft of torque at the wheels, which equates to 6hp!
Answer: Horsepower is King! (the more horsepower the more torque at the wheel)
Back to the large and small engine example at the beginning, which will accelerate a car down the quarter mile the quickest? They both put out the same torque at the wheel, so I guess as the small engine is considerably lighter, it's the winner. Again its not quite as straight forward as that. What we are really interest in is the average torque at the wheels through out the complete run. High revving engines by there very nature have a small power band, in other word there torque curve is not very flat compared to large displacement engines. To keep the average torque at the wheel as high as possible we need loads of gears, and changing gear takes time. So to counter its weight disadvantage the large displacement engine has high torque through out the working rev range, therefore needing less gears. Never straight forward is it!
There you go, Torque v Horsepower according to my world!
If you have any comments please let me know, good or bad, this is a working document.