Relation Between Torque and Speed

Like so many things in engineering, there is a simple answer which is not completely right and a correct answer which is not simple.

Theoretically, since P = ωT, torque and speed are inversely proportional. However, the situation gets complicated by the fact that internal combustion engines have speed-torque curves that don't follow this formula very well, and they tend to have maximum power at a higher speed than where they have maximum torque. At high speeds and low speeds, they are terrible. So, we use transmissions to try to find a gear ratio that allows us to make the best of the situation. Big trucks frequently use maybe a dozen gear ratios so they can stay close to the maximum power point and some equipment in recent years use infinitely variable hydraulic transmissions to the same end.

rcm_mech didn't mention power! Blink gave 1 ft lb @ 5252 rpm = 1 hp. Also 5252 ft lb @ 1 rpm would = 1 hp. Therefore, the relation between torque and speed is a continuum between and beyond the example numbers.

I would prefer to think of torque and speed as independent variables--they have nothing to do with each other. Both can be high numbers, and then you would have a bunch of power; or both low numbers with negligible power.

Torque measures the twisting force, and speed measures how fast it is going--either translation or rotation. Lots of torque can produce large accelerations. Very high speeds probably require high torque to overcome windage, friction, etc.

that description was really very helpfull

with 1' radius wheels, this would equate to 5233 feet per minute

You mean about 2616 feet per minute...

I fear you have confused radius with diameter. 2 x 3.14159 x 833 = 5233.88. Please self-administer 40 lashes.

Forget about torque or all you will do is confuse yourself. You can get any torque you want with the right gearing.

You are assuming that the OP is easily confused --- which he may find insulting.

Torque and horsepower are entirely different concepts, the first of which does not require any motion. In any engine that has a rotational output, horsepower is impossible to achieve without torque, so it is not something that can be forgotten.

It is only true that you can get any torque you want with the right gearing if you are willing to accept a wheel speed that you do not want. If your old VW is going 60 mph, there is no gear you can select that will enable you to maintain that speed up a 20% grade.

The calculations one generally does for aero resistance, rolling drag and grade climbing all result in forces needed to overcome these. These forces are balanced or overcome by tractive effort, which translates directly into wheel axle torque, (given a wheel radius).

For a given HP, gearing allows you to trade speed for torque. Therefore, you cannot simply forget about torque. Torque is as central to the discussion of what allows a vehicle to go up hill at a particular speed (or accelerate at a particular rate) as any other element.

Blink -- With all due respect to your excellent explanations given to many of the CR-4 forum topics --

I've found, through years attempting to give simple engineering explanations of what fellow racing enthusiasts see and ask, as soon as I start talking "torque" with respect to motion I find myself trying to get the listener to keep rotational speed in his mind at the same time. This is hard for many people who lack the visualization talents that most of us engineers have. I could never come up with an explanation of how torque relates to speed against a load that people could grasp easily and didn't confuse myself.

IMHO it's best to talk about torque (or force) when the issue is about breaking something or initiating movement; gearing when the issue is speed; power when the issue is motion against a load; and energy when the issue is about the net results of an event. (and I'll grant here that energy is hard for most people to visulize unless you can put in terms of money)

So I figure that if it confuses me it will confuse someone who knows less than me and someone who knows more ought to be able to rise above the level of being insulted by such as myself.

Ed Weldon

Sorry gentlemen, but horse power is an arbitrary, calculated value. It is merely torque x time over distance. It is totally theoretical and was a way to compare a steam engine to the work a horse was capable of. Power cannot be measured, only torque, distance and time can.

If so, does that mean that if I think I have more power, I will have more power? And vise versa.

Power cannot be measured

I will have to remember to throw out my wattmeter.

It is merely torque x time over distance.

Or to illustrate with English units: (lb x ft x seconds) / ft = lb-seconds. Hmmmm. I'd guess I'd have to agree that your concept is entirely theoretical.

A gearbox is a "Torque Multiplier", and a HP reducer. Horsepower was created as a means of relating the "work" done by the new steam engine to something people could relate to, a horse. Horsepower is a measurement of "work", thus the time component.

Force is a vector, acting straight line. The bmep acting on a piston is linear, pushing the piston down the bore (assuming a common IC engine). This force is converted to a "moment" via the crankshaft throw. This moment or torque is transmitted via the drive train which includes "torque multiplication" to the rear wheels where the resulting moment is converted to a force via the tyre's contact patch. This force reacts with the road surface producing forward motion.

The twisting force or torque acting on the axle via the rolling radius of the wheel/tyre is what produces instantaneous acceleration. Horsepower does NOT and cannot cause any instantaneous acceleration.

Look up what horse power is and you'll see that it is a representation of the work done by a motor, not its ability to generate a force.

This has been described in this topic previously.

A gearbox is a "Torque Multiplier", and a HP reducer.

Did you mean speed reducer? HP is not changed by a gearbox, other than by frictional losses, which tend to be small.

Horsepower does NOT and cannot cause any instantaneous acceleration.

However, torque alone, which does not imply motion, cannot cause anything but instantaneous acceleration, and stringing a series of instantaneous accelerations together into usable acceleration requires horsepower. For acceleration there must be movement, and it is the engine's rotation which causes this movement. The instant there is any movement, there is rotation, and therefore rpm, and therefore HP.

You can predict useful acceleration (e.g., 1/4 mile times) from hp to weight ratios but not from torque to weight ratios. You can also achieve an instantaneous acceleration from an engine of any torque output, via appropriate gearing. (You can also climb a hill of any grade.) But to achieving more than instantaneous acceleration requires hp, as does driving up a hill at a particular speed.

Another take on this:

When I calculate the top speed of a vehicle, I balance the various drags vs the tractive force in e.g, pounds. Tractive force relates directly to engine torque (times overall gear ratio/tire radius) so one could say that top speed, at any instant, relates directly to engine torque. However it is HP that measures the fact that this torque is being delivered at some rpm, and only through RPM do we have actual motion.

But in any case, the either-or argument is fallacious, just as is would be silly to argue whether voltage or current is required to cause acceleration.

Any 440 calculator that uses HP as an input will HAVE to convert that HP into torque. That is why they need RPM. Horsepower is always calculated. I know may are misinformed but this is the fact. When estimating the acceleration of a vehicle, the basic inputs are torque, driveline loses, mass, coefficient of friction (tyre grip), frontal area and coefficient of drag.

Horsepower is a calculated representation of work done. To accelerate a body, "force" is required. Torque is force time distance, or a moment, and can derive the force ant the contact patch leading to calculating acceleration by f=ma.

Any 440 calculator that uses HP as an input will HAVE to convert that HP into torque. That is why they need RPM. Horsepower is always calculated.

Untrue. Here's one of a zillion typical calculators that goes from car weight and horsepower directly to 1/4 mile time.

We use torque in calculations because it is convenient, and because wheels are driven by axles which are twisted by an engine and transmission. But we can calculate the acceleration of an airplane down a runway based upon hp alone, and can calculate the acceleration of a horse, based on horsepower alone. The F in F=MA, when applied to cars, is tractive force, a linear force that could be replaced by a rope being pulled by loads of horses, or by a jet engine. Torque is a calculating convenience, and is the straightforward means to finding out if you have enough tractive force to either achieve, maintain or exceed a target speed -- but it is not an essential requirement for calculating acceleration.

One can get essentially perfect accuracy by this method (using hp), if instead of estimating the effect of aerodynamic drag and rolling friction, you use actual values for each increment in the calculation.

When estimating the acceleration of a vehicle, the basic inputs are torque, driveline loses, mass, coefficient of friction (tyre grip), frontal area and coefficient of drag.

Sure. Those are some of them. However, without knowing the engine rpm at which a given torque is produced, you cannot know whether or not acceleration can be carried on beyond a given speed. (And if you know engine rpm and torque, then you know hp.) If the speed in question cannot be exceeded by the available hp, acceleration stops. Tractive force used in the F-=MA calculation is the net, not gross tractive force, and that cannot be calculated without knowing both rpm and torque (and thereby calculating an appropriate gear ratio, and from that and wheel radius calculating tractive force), and then subtracting at each increment in speed, the aero and rolling drags.

A 40 hp VW beetle in first gear will out-accelerate (sustain a higher G force than) a 400 hp Ferrari in 6th gear, and a lawn tractor can match either up to about 3 mph. But the acceleration of the Ferrari at each instant in a 1/4 mile run is dramatically higher than that of the VW. When the VW gets to 72 MPH, it can accelerate no longer accelerate (an hp limit); when the lawn tractor reaches 4 mph, it can no longer accelerate (a gearing limit).

If the discussion is about engine hp and engine torque, then it is easy to show that a difference in acceleration is due to a difference in HP not torque. In physics devil's answer to a question I posed in another thread, he shows that if two motors have the same torque but different hp (in this case the hp ratio is 2:1), the acceleration will vary by the ratio in hp. (In other words, the vehicle with double the hp reaches 60 in half the time.)

you're getting bogged down with semantics and you'll just go in circles. Get back to basics, a force applied to a shaft via a radius is a moment and this moment is torque. Horsepower is work done and because speed is involved is mainly useful calculating gear ratios (the torque multiplier).

Please look up what horsepower is, a representation of work. One horsepower is 550 lbs lifted over 1 foot in one second. Distance over time is speed last time I looked so speed (or velocity) is directly related to HP. Without speed, no HP.

Please look up what horsepower is, a representation of work.

Hp is a measure of power.

Without speed, no HP.

Sure. And a car cannot reach any speed without tractive force, which relates directly to torque.

A perfect analogy is seen in electric motors (and electrics in general). Voltage x Current = power. One never argues (sensibly at least) about electric power requiring either voltage or current. One cannot say that either hp or torque is required for acceleration, if the prime mover is an engine. However, one can calculate accelerations based only on hp but not based only on torque... because engine torque alone does not tell you if you have enough hp to exceed any given speed. You can say that acceleration = power/(mass x velocity).

Looked at another way, a 5 hp lawnmower engine with internal gearing for a PTO could be in a black box, with an output shaft having any desired torque -- lets say 200 lb-ft (obviously at very low rpm). A 300 hp racing engine can also have a maximum torque of 200 lb-ft. The two "engines" are putting out identical torques, but one will produce a far better 1/4 mile time than the other.

Speed torque invrsly proportional relationship holds good when applied force is fixed. Most of the control systems adjust force to retain speed for different torque requirements. Torque may be a dynamic parameter for which speed need not change and this is done simply by applying more force or by supplying more energy.

Torque is a force and speed is the rate of change of position. You need to be more specific, i.e. do you want to know how much torque to climb a steep road at a certain speed?

Let me attempt a simple answer. Torque is nothing but the pulling required. Which means a higher torque is needed on uphill drive. The formula covering this is that HP=2*3.14*N*T / 4500 , which implies that T(Torque) and N (Speed) are proportional. i.e. For a specific HP of the Engine, if the Torque needed is more, the speed has to be less. That is why in uphill, we turn to a lower gear to have more pulling at a reduction in speed. In plains, since the torque needed is less, we can raise the speed. Hope this is making some meaning ?

Either is appropriate if what you want to do is lift the truck (drive it uphill) at a constant rate of speed and ascent.

Knowing the torque curve of the engine and the load imposed by the truck you can calculate an appropriate gear ratio. Of course, in the real world the engine may not have the torque required at the RPM required to reach a particular speed. The horsepower will be whatever the engine is making at that RPM. Gearing changes torque but not horsepower.

If you know the rate of ascent and the weight of the truck you can calculate the horsepower required. Again, in the real world the engine may not be capable of "lifting" the weight at a particular rate.

Accelerating the truck is a bit more complicated. For that you would use the torque curve of the engine, or calculate the torque curve from the horsepower curve. This may help:

http://spreadsheets.google.com/ccc?key=0ApPRT4wdrOMvcEJDSDJDbHptcnBsSFVORmdya1Q3SEE&hl=en