KW to HP Formula Conversion

[DickDV]

I can't seem to make the numbers come out converting the HP formula (ft-lb x rpm/5252) to KW (N-m x rpm/9549).

If I substitute .746kw for hp and N-m/.74 for ft-lb I get

.746kw = N-m/.74 x rpm/5252

Solving for kw I get N-m x rpm/2899

What am I doing wrong?

 

[thinker]

And what about the following definition: One horsepower is a power developed by the horse having a length of 1 meter and a weight of 75 kilograms?

 

[cswilson]

This discussion reminds me of an assignment I had in junior high school physics class when we were studying power. We had to weigh ourselves, get timed in the 50-yard dash, then calculate how much power we generated doing so.

My calculations went something like this:

(150ft * 100lbs) / 8 sec * (1HP / 550ft-lb/sec) = 3.4HP

This was the type of calculation the teacher wanted, but it left me scratching my head, because I knew that a "horsepower" was fundamentally based on the power a horse could generate, and here I was, the proverbial 98-lb weakling (I was a runt in junior high) generating more power than 3 horses! It wasn't until some years later that I figured out the problem with the calculations.

Actually, it was a useful "life lesson" as it sensitized me to issues of mass and force, and taught me that authority figures often get it all wrong.

Curt Wilson
Delta Tau Data Systems

 

[davidbeach]

Curt, I think that the biggest problem was that you produced 3.4 gross HP, while the standard calculation based on what a horse could theoretically do results in a net HP value. The horse moving the weight of the horse is entirely omitted from the standard equation. Had you tried to make your 50-yard dash while restrained by a 100 lb force you would have taken far more than 8 seconds.

 

[cswilson]

David,

The horsepower unit was originally set by having a horse walking horizontally but with a rope pulling a large weight vertically up a mineshaft. The power the horse expended in moving its own mass horizontally was relatively trivial, and so not accounted for.

Similarly, in my stupid junior high experiment, I did not have to exert anything close to 100 pounds-force to move my 100 pounds-mass horizontally, and was not generating anywhere near 3.4HP. So the biggest issue was not gross versus net.

When I later figured out what was wrong with my teacher's analysis, I thought of two variants of the experiment that would have been more accurate. First, we could have been timed climbing a ladder up a wall of the school (it had one). Second, we could have walked on the roof of the school while tied to a weight we were pulling up the side of the school over a pulley, just like that original horse. Sadly, I don't think either of those experiments would have been feasible.

Curt

 

[IRstuff]

Actually, it's another reason to use something like Mathcad, which is unfortunately very expensive at its list price, but it does unit conversions completely transparently to the calculation.

type: hp = , result is 745.7W

change units to ft*lbf*2*pi/min, results in 5252.1
change units to N*m*2*pi/min results in 7120.9
N*m = 0.7376 ft*lbf

This is sort of related to a similar posting about engineering software programs. The fact that people state that they are continually making conversion errors is really a sign of a seriously missing tool in the panoply of accessible engineering tools. With a good tool, the conversions are irrelevant, and the unit system can be pretty much anything anyone wants, like:

hp = 71362 N*furlongs*2*pi/fortnight

The effort to this conversion is, in something like Mathcad, exactly the same as using any other unit system, other than the extra typing keystrokes for the longer unit names.

TTFN

FAQ731-376

 

[7anoter4]

My opinion is that one has to stay all the time in the same units system.
As burnt2x said: P=T*W W= 2*PI()*rps rps=rpm/60
In Metric Units:
T[N*m]=P[w]/2/pi()/rps T[N*m]=60*P[w]/2/pi()/rpm
1 kw=1000 w T[N*m]=60000/2/pi()*P[kw]/rpm
60000/2/pi()=9549.297 then : T[N*m]=9549.297*P[kw]/rpm
Now in British Units:
1 HP=0.746 kw
As IRstuff said 1 N*m=0.7372979 ft*lbf then:
T[lbf-ft]=0.746*60000/2/PI()*HP/rpm*.7372979 =5252.345* HP/rpm

 

[vinnygalbo]

Good thing is most european manufacturers now offer datasheets / tech specs in both metric & american standards.