# Regarding the measurement of horsepower

I teach aerodynamics. One horsepower is 550 lbs moved one foot in one second.

My question is this. Does that assume that the 550 lbs is being lifted vertically against gravity? As opposed to moving, say, a 550 lb chunk of concrete across a floor.

And if so, does the gravity value of 32.2 ft per second per second effect the measurement when gravity changes?

Tex

• Likith D

mjc123
Homework Helper
Yes, it is lifted vertically.
And no, the 550 lb force is constant. If g varies, the mass required to give 550 lb weight will vary, but the definition remains 550 lb weight.

russ_watters
Mentor
I teach aerodynamics. One horsepower is 550 lbs moved one foot in one second.
No, the definition of horsepower is a force of 550 lb applied over a distance of 1 ft in one second. I think that should be sufficient to clarify the rest you were confused about.

russ_watters
Mentor
Yes, it is lifted vertically.
Note that historically (in the wiki) the first reference, prior to James Watt, was indeed of lifting water. However Watt defined it in terms of pull force and linear motion, which is more general/accurate.

• sophiecentaur
anorlunda
Staff Emeritus
Note that historically (in the wiki) the first reference, prior to James Watt, was indeed of lifting water. However Watt defined it in terms of pull force and linear motion, which is more general/accurate.

That's true, but we should also point out that the force needed to pull a 550 pound block horizontally across the floor depends on friction, and in most cases will be less than 550 pounds.

russ_watters
Mentor
That's true, but we should also point out that the force needed to pull a 550 pound block horizontally across the floor depends on friction, and in most cases will be less than 550 pounds.
Of course; that's why horsepower is defined according to the force, not the mass or weight of the object it is being applied to.

So, in effect...

If I apply a measured force of 550 lbs to some unknown something and the work produced is one foot of movement in one second, I will note that the total opposing force including drag or friction plus inertia will be 550 lbs. that could be a 1 lb nerf ball with an additional 549 lbs of opposing force.
Tex

anorlunda
Staff Emeritus
So, in effect...

If I apply a measured force of 550 lbs to some unknown something and the work produced is one foot of movement in one second, I will note that the total opposing force including drag or friction plus inertia will be 550 lbs. that could be a 1 lb nerf ball with an additional 549 lbs of opposing force.
Tex

Now you took something very simple and made it complicated enough that I can't understand the above.

If you make a 550 pound force (Measure it by tension on the rope. That includes a force pulling and a force resisting.) over a distance of one foot in one second, that is 1 HP. #### Attachments

phinds
Gold Member
2021 Award
So, in effect...

If I apply a measured force of 550 lbs to some unknown something and the work produced is one foot of movement in one second, I will note that the total opposing force including drag or friction plus inertia will be 550 lbs. that could be a 1 lb nerf ball with an additional 549 lbs of opposing force.
Tex
No, that is not correct. If the nerf ball experiences no friction then it would not enter into your calculation so the result would be 549/550ths of a HP. Listen to what people are telling you. It is NOT the weight/mass that enters into the calculation, it is just the force. If your 1lb nerf experienced 10lbs of friction that had to be overcome then your example would result in 559/550ths of a HP

• russ_watters
sophiecentaur
Gold Member
I have read this thread and it seems a further good reason for switching to SI Units. A Force is a Force and a Mass is a Mass in SI. If you are lifting a load or pushing it across a rough horizontal surface the Force will be in Newtons and the Power will be the Force times the Speed.
Pounds Mass, Pounds Weight and Slugs is a world I would rather not venture back into. I left that world in about 1959, iirc and took the long route to SI via cgs and mKs during my education years.
No, that is not correct. If the nerf ball experiences no friction then it would not enter into your calculation so the result would be 549/550ths of a HP. Listen to what people are telling you. It is NOT the weight/mass that enters into the calculation, it is just the force. If your 1lb nerf experienced 10lbs of friction that had to be overcome then your example would result in 559/550ths of a HP
I found this as confusing as the post you are responding to. This can't go far without some diagrams with labels, numbers and arrows on.

• CWatters
My point is this.

If there is a huge slab of concrete weighing several thousand lbs. and I apply a measured force of 550 lbs and move that block one foot in one second then I only did the work of one horsepower. In other words...it doesn’t depend on the weight of the object...it depends on how much force is applied and the distance and time.

We can argue or debate WHY or HOW a two thousand lb block moved a foot but what matters is that it DID move under the force of 550 lbs, it moved one foot, and did so in one second. So one horsepower of work was done.

Correct?

Perhaps another way to clarify (or confuse) the issue is that one horsepower is (roughly) equivalent to 746 Watts. No reason to look at them really as anything other than Power defined in terms of different units/quantities. i.e. It is pretty much just an expression of a quantity of Power. The historical definitions are just a way of quantifying a consistently describable amount. The definition of power remains the same (Work / time) no matter how we quantify the units.

diogenesNY

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Dale
Mentor
2021 Award
it doesn’t depend on the weight of the object...it depends on how much force is applied and the distance and time.
Yes, exactly

FYI..

This comes up in aerodynamics all of the time.

If there is 60 excess BHP available, determined between the power required at a given airspeed and the power available, then a aircraft of a certain weight can be expected to climb at a rate calculated from that excess BHP and weight. This is also used in cruise performance calculations.

Tex

• Tom.G
sophiecentaur
Gold Member
I apply a measured force of 550 lbs and move that block one foot in one second
This bare description could be more precise because it suggests that the block starts of stationary. What should be included is that you would be maintaining the speed of the block at one ft per second. A motor with less than 1hp (or a weak, feeble human) can sustain the speed of a canal boat of many tons so that it does one foot per second. However, it can take several minutes to reach that speed from stationary.
In most of Physics, it is essential to state the conditions precisely if you want to avoid the wrong implication. jbriggs444
Homework Helper
We can argue or debate WHY or HOW a two thousand lb block moved a foot but what matters is that it DID move under the force of 550 lbs, it moved one foot, and did so in one second. So one horsepower of work was done.
An average of one horsepower of power was provided by the 550 pound force over the course of that second. 550 foot-pounds of work was done by the force.

Other forces such as friction, gravity, normal force and three other helpers also pushing may have acted. But what matters for the work done by the 550 pound force is that it was applied and that the object moved one foot in the direction of the force while it was applied. The elapsed time then matters for the "power" -- the rate at which work is supplied.

• sophiecentaur
sophiecentaur
Gold Member
it was applied and that the object moved one foot in the direction of the force while it was applied.
Yes. You often need to provide appropriate extra conditions for the force to achieve the Power input to the system.

Tom.G
Gold Member
FYI..

This comes up in aerodynamics all of the time.

If there is 60 excess BHP available, determined between the power required at a given airspeed and the power available, then a aircraft of a certain weight can be expected to climb at a rate calculated from that excess BHP and weight. This is also used in cruise performance calculations.

Tex
Sure looks good to me!

anorlunda
Staff Emeritus
A Force is a Force and a Mass is a Mass in SI.

Don't you use both kgf and kgm? When buying meat by weight in Europe, does the scale indicate kg or newtons? Is the price quoted in kg or newtons?

• russ_watters, Tom.G and phinds
sophiecentaur
Gold Member
Don't you use both kgf and kgm? When buying meat by weight in Europe, does the scale indicate kg or newtons? Is the price quoted in kg or newtons?
NEVER.
The unit of Force is the Newton in SI. When we buy meat or veg, then we, of course, want to buy it by Mass (how much of it there is) and we usually measure that by the effect of the Weight force on a spring or piezo crystal. We also, sometimes, compare the weight force of the leg of lamb against the weight force of some standard brass masses.
PS Can you find and quote any authority that implies this?

jbriggs444
Homework Helper
NWhen we buy meat or veg, then we, of course, want to buy it by Mass (how much of it there is) and we usually measure that by the effect of the Weight force on a spring or piezo crystal. We also, sometimes, compare the weight force of the leg of lamb against the weight force of some standard brass masses.
This is, of course, also exactly how things are done in the U.S. We buy meat and vegetables based on a mass standard, not based upon a force standard.

• sophiecentaur
sophiecentaur
Gold Member
This is, of course, also exactly how things are done in the U.S. We buy meat and vegetables based on a mass standard, not based upon a force standard.
Which makes sense. The problem is when the Pound Force is confused with the Pound Mass. At school, we used the Poundal (Force to accelerate one pound mass at 1 ft/s2). That made sense to me at the time but no one ever used the Poundal in everyday conversation - Otoh, Newtons are used by everyone to describe Forces.

• jbriggs444
anorlunda
Staff Emeritus
When we buy meat or veg, then we, of course, want to buy it by Mass (how much of it there is) and we usually measure that by the effect of the Weight force on a spring or piezo crystal. We also, sometimes, compare the weight force of the leg of lamb against the weight force of some standard brass masses.

Just a bit of playful kidding sophie. It is no different in English units. Measuring mass by the force on a scale is what led to the terms pounds-mass (lbm) and pounds-force (lbf). I see no difference SI or English in that regard.

I think the accurate way to express it is that the SI system never confuses mass with force, but also that the pure SI system is not actually used in everyday life.

• sophiecentaur
jbriggs444
Homework Helper
Measuring mass by the force on a scale
We measure lots of things by using proxies. We measure wind speed by the rotation rate of a turbine. Or current by the deflection of a needle on an arm attached to a spring under the influence of a magnetic force. Or voltage by the deflection of the exact same needle under a different set of conditions.

The underlying confusion is in conflating the proxy with the quantity being measured.

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russ_watters
Mentor
...and we don't necessarily always have a clear picture of the limitations of the proxy...or even of the proxy of the proxy of what you are really after. A consumer scale may not be corrected for gravity's variation, but a commercial/scientific one is.

@jbriggs444 I'm not sure if I agree with your examples though because I consider internal functions of the device to be a separate issue from what "thing" is being applied to it to measure. A scale that reads out in mass is nevertheless *actually* measuring force, regardless of what the readout units are. We often use such scales for experiments to measure force and then back-convert if needed (if English, no conversion needed), for that reason.

Let's explore your wind example. The wind vane, if I understand them correctly, is directly sensing wind speed. The rotation rate of the vanes is motion and even if converting motion from linear to rotational, that's not really changing anything relevant. My understanding is that because it is a direct measurement, it is not subject to variation due to density (though I'm not certain).

But consider instead a pitostatic tube. It measures (is connected to a device that measures) pressure, not speed. In my industry, sensors often come with multiple input devices to the same readout device and include multiple modes for converting proxies into what you really want to know in the readout; pressure, velocity, or volumetric flow rate can all be read from the same pressure measuring device.

But even for HVAC, where we do most of the final work in terms of volumetric flow rate, that's still another proxy for what *really* matters most of the time: mass flow rate. That can be a problem if we rarely think about that second-level proxy and then have to deal with a change in air density.

My understanding (not totally certain) is that they deal with the issue in airplanes from the opposite direction, by accepting that the proxy - airspeed - is more a reading of mass flow rate than speed, even though it is called a "speed".

There are other fluid speed measuring devices that use doppler shift to measure the speed of suspended particles. We can set those aside for now though because their principle of operation may contain other proxies...

My point either way is that we don't always think about these issues when not in a professional context, but when we are, these issues can matter a lot.

Edit: ...I suppose the internal vs external proxy thing can be a bit arbitrary of a distinction though: my understanding is that multimeters use some internal proxies, such as voltage drop across a known resistor for current.

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jbriggs444
Homework Helper
I'm not sure if I agree with your examples though because I consider internal functions of the device to be a separate issue from what "thing" is being applied to it to measure.
Where does one draw the line between internal functions of the device, calibrations of the device, and corrections due to transient conditions? Coming from a somewhat mathematical point of view, my preference is to abstract away all of the implementation details and consider a scale as an abstract mass measurement device regardless. Someone coming from an experimentalist point of view would obviously have very dissimilar preferences.

• russ_watters
anorlunda
Staff Emeritus
The issue is not physics or measurements. It is natural language. Not language that we use at work, but what ordinary people use in the market.

It is not reasonable to demand that the entire public should use words in the way scientists define. Nobody ceded to science the authority to declare how common words are defined. When we need a precise definition, it is better to coin an entirely new word that has no natural language meaning. Hertz and software are examples.

• The same could be said about everyday use of many units. But we wouldn't ever use the 'everyday' in any other discussion on PF (would we??? ). The good thing about the Newton and the Kg is that the words sound nothing like each other and they do not need suffices to distinguish them.