# Torque HP Speed

### What Is Torque, What is HP?

[CT] Torque is basically the rotational equivalent of a force. In that sense, torque can be thought of as the potential to

` do work. `

But just as a force can only do work by being applied through some distance, torque can only do work by being applied through some angle. The rpm is simply the rate at which that angle changes (i.e., the rate of rotation).

Power is the rate at which the torque is doing work. Technically, power = torque * rotation rate, but usually some constant is included to correct for a convenient choice of units.

For example, if power is expressed in units of "hp", torque is in "lb-ft", and rotation rate is in "rpm", then power = torque * rotation rate / 5252. That constant (5252) will change depending on which units are chosen for power, torque and rotation rate.

[AWN] Torque is the product of a force and its moment arm. That is, Torque = FR, where F is the force in pounds and R is the length of the moment arm in feet.

Work is, for our purposes, the product of a force and the magnitude of its displacement. That is, Work = FS, where F is the force in pounds and S is the displacement in feet.

Power is the rate at which work is performed: Power = Work/Time. We’ll measure time in minutes.

Dynamometers can measure torque, in foot-pounds; they can NOTdirectly measure horsepower. To calculate horsepower, we have to combine the torque measurement with a time measurement. Here’s how:

A long time ago, before any of us (except maybe Harry Somerfield and Don Jewett) were born, James Watt performed some experiments and determined that a horse could lift 550 pounds at a rate of 1 foot per second. This unit of power, 550 foot-pounds per second, became known as the "Horsepower."

Since I already said that we’d be dealing with time in MINUTES, not seconds, we can multiply by 60 seconds/minute to get: 1 Horsepower = 33000 foot-pounds/minute, which implies that a horse can list 33000 pounds a distance of one foot in a minute, or launch a one-pound weight to a height of 33000 feet in the same time. No mean feat. But I digress.

To calculate an engine’s horsepower at some given speed, you do the following: Rev the engine to the desired speed. Measure the torque at that speed. Multiply the torque by 2 * PI * the engine speed in revolutions per minute. This gives you:

X foot-pounds * 2 * PI * REVOLUTIONS

` -------------------------------------------------------`
` MINUTE `

Which, if you look closely, is a FORCE (in pounds) times a DISTANCE ("one foot * 2 * PI * revolutions" is the distance the tip of our one-foot moment arm travels, in feet) divided by TIME (in minutes).

As we know, FORCE times DISTANCE divided by TIME = POWER.

We now have power expressed in foot-pounds per minute. To convert to horsepower (33000 foot-pounds per minute, remember), we simply divide by 33000. So Horsepower =

Torque * 2 * PI * RPM

` -----------------------------`
` 33000`

Torque * RPM

` = ----------------------`
` 33000/(2*PI)`

Torque * RPM

` = ----------------------`
` 5252`

Which, incidentally, implies that an engine’s torque and horsepower curves cross at 5252 RPM.

1 hp (Metric) = 0.986320406 hp (550 lbf.ft/s)

` 1 hp (550 lbf.ft/s) = 0.745699872 kW `

There are two forms of drag on a car; rolling resistance and aerodynamic drag. Rolling resistance (tyres and drive train losses) increases slowly, but constantly with speed. Aerodynamic drag increases as the square of the speed (V in km/h) and power required to overcome that drag increases as the cube of the speed.

Power (Kw) = rolling resistance + V^3 Cd A / 76716 + rolling resistance

The number 76716 is a conversion factor accounting for air density at sea level and converting from m/s to Km/h. The frontal area A of the CRX is about 1.7 square meters. With a drag coefficient (Cd ) of 0.31 and estimating rolling resistance would absorb about 6 Kw at speed, lets have a look at the power required to achieve at 240 kph.

Power (Kw)

# 240 * 240 * 240 * 0.31 * 1.7 / 76716 + 6

101 Kw

You can calculate the frontal area by parking the car against a concrete wall at night and using a spotlight and someone to help trace the outline of the car. The shadow can then be measured to give the frontal area. Simple things like removing the wing mirrors reduces the frontal area by 1% which increases the top speed by 1%. Lowering the car by 2 cm reduces the frontal area by 1 % and reduces the drag because the body covers more of the wheels. These two procedures alone add about 5 km/h to the top speed.

Increasing the power of the car by 30 % would only add about 10% to the top speed of the car, as would reducing the drag by 10 %.

### Have HP Calculations Changed?

This is how horsepower is calculated now, and it’s how horsepower has ALWAYS been calculated. Now there ARE a couple of different ways to set up a dynamometer. Specifically, the SAE and DIN organizations have different rules about which engine accessories must be running while dyno testing is performed. However, these differences have NO effect on the actual torque-to-horsepower conversion.

### What Factors Affect Top Speed?

[AWN] Many factors affect top speed. Weight (except very indirectly) is not one of them. Think about WHY there’s a top-speed limit at all (i.e. How come you can’t just put a really tall 5th gear in a car and accelerate all the way up to 600 MPH or beyond?)

The reason is friction, of which there are three main sources: Aerodynamic drag, losses through the transmission, and tire friction. The loss from each of these sources increases geometrically with increased speed. Eventually, you reach a point where all the engine’s power is being used to overcome these losses, so none is left over for acceleration.

Weight affects none of these drag sources except tire friction, and even then, its effect is almost COMPLETELY overwhelmed by aerodynamic losses. If you loaded up an NSX with a couple tons of lead, it’d only drop the top speed by maybe 10 MPH or so.

### Just how big were those horses anyway?

#### by Dennis Simanitis

The power of horses came up recently in a chat with longtime reader Bob Michaud (kin by marriage to R&T’s late Nat Michaud, by the way). In particular, he’d heard recent tub-thumping about today’s 300-bhp sedans harking back to the glorious days of the Fifties.

"But aren’t today’s engines even more impressive?" he asked, "because now it’s net horsepower and back then it was gross."

Yep, was it ever.

We both did some research on this technicality in the pages of our favorite enthusiasts’ magazine, and here’s what we learned.

By background, and worth repeating periodically for new readers, an engine’s output is measured on a brake dynamometer, hence the term "brake horsepower." As its name suggests, this gizmo is essentially a giant brake that resists the rotation of the engine’s crankshaft, this twist measured in our English system in lb.-ft. of torque (think of a 1-lb. weight suspended from the end of a 1-ft. ruler).

Horsepower and torque are related by the formula:

` bhp = torque x rpm/5252`

Lurking here is the fact that 1 horsepower is defined as 550 ft.-lb. of work expended in 1 second; engine revs are ordinarily measured per minute; and pi, approximately 3.1416, crops up through angular velocity relating ft.-lb. of work and lb.-ft. of torque (conceptually two different things with similar names). Succinctly, 5252 = (550 x 60)/2pi.

So, for instance, suppose an engine produces 450 lb.-ft. of torque on the dyno at 3,500 rpm. This equates to:

` (450 x 3500)/5252 = 300 bhp`

A nice round figure, 300 bhp.

And this brings us to Bob Michaud’s observation, because the real question is, "Under what conditions was the engine operating when it produced that torque?"

Equivalently, "Just how big were those horses, anyway?"

There were, and continue to be, relevant standards for horsepower measurement, originally J245, now J1349 and J1995, promulgated by my old employer, the SAE. In fact, they list two different measurements, net and gross. (I warned you.)

Succinctly, gross measurements are taken with a stripped engine running only its internal ancillaries such as fuel pump, oil pump and water pump. By contrast, net measurements require a fully equipped engine fitted with all of its accessories, generator/alternator, starter, emissions controls and a full exhaust system.

Obviously, each of these components robs a tad of power. Engines evidently differ, but generally, gross bhp ratings may be as much as 40 percent greater than net.

And, indeed, let’s harken back to the glory days of the Fifties. Ford certainly learned that safety didn’t sell diddly in 1956; Chevy’s new V-8 ruled. Until the Chrysler Hemi came along. And the Ford V-8s.

The Horsepower Race was on, gross figures were the norm, and competitors should be excused if these ratings got a trifle exaggerated. As some suggested, bhp meant "horsepower at the brochure."

This continued into the Seventies, which somehow or other turned Socially Conscious. (Don’t look at me; I was fooling around in the Virgin Islands.)

The automotive upshot came in 1972 — and, wouldn’t you know, first in California. In R&T, February 1972, my Engineering Editor predecessor, Ron Wakefield, cited a new state law requiring that all automakers henceforth use net ratings in any advertising, brochures or manuals of their motor vehicles.

As usual in such things, California led the nation, we all became less gross, and the rest is history. Until, of course, today’s 300-bhp sedans that Bob Michaud and I were discussing.

Let’s celebrate a real 300 bhp!