# Need to calculate mass to potential horsepower

I need to calculate how a mass (of an unknown weight) suspended on a pulley and shaft, what would be the weight in lbs (or Kg for that matter) to give me a 50 hp output using a series of gear reducers going from less than 1 rpm to the input shaft and a final output rpm of 1850. the configuration of the 3 or 4 gear reducers is is such that the ratios of each gear reducer can be varied. So long as the final output is 1850 rpms and 50 hp. please help.

cjl
That depends on the size of the pulley. If the pulley is sized such that the mass is descending at 1 m/s for example, the mass will need to be about 3.8 metric tons. If you want the mass descending more slowly (which I assume is the case, given your 1rpm input), you'll need more mass. For 10 cm/s for example, you'll need 38 metric tons. The output shaft speed is irrelevant in this case - you can gear it to provide the output speed based on the input (although you'd need some kind of governor to keep the speed constant) - the only important factors are the desired power and the speed at which the mass is descending.

38 metric tons? I think you may be way off on your calculations my friend, Im no phyics person and dont claim to be, but common sense tells me that just aint right. Thanks for help tho much appreciated, god bless.

Nugatory
Mentor
38 metric tons? I think you may be way off on your calculations my friend, Im no phyics person and dont claim to be, but common sense tells me that just aint right. Thanks for help tho much appreciated, god bless.

That was 3.8, not 38, and 3.8 agrees with my calculations.

cjl
That was 3.8, not 38, and 3.8 agrees with my calculations.

38 if you want the mass descending at 10 cm/s (I did mention that as an option as well).

As for common sense? It can prove surprisingly unreliable in situations like this. The reason such a large weight is needed is because of the low input RPM (and thus, the low velocity of the mass). Most 50-ish horsepower motors provide their power at a fairly high speed, and thus the forces involved are much smaller.

just don't see it, i,ve been told by many engineers that it would only take around 1800lbs to have enough force from gravity pulling down from the pulley to rotate the shaft and have 50 hp to output on the final gear reduction. but just trying to confirm it. i guess to make my question simple, how much downward force in lbs is needed to equate to 50 hp?

cjl
just don't see it, i,ve been told by many engineers that it would only take around 1800lbs to have enough force from gravity pulling down from the pulley to rotate the shaft and have 50 hp to output on the final gear reduction. but just trying to confirm it. i guess to make my question simple, how much downward force in lbs is needed to equate to 50 hp?

As I said in my first reply, it depends on how fast the weight is descending. To use non-metric units, a horsepower is equal to 550 lbf*ft/s, so a 550 pound weight descending at 1 ft/s would give 1 horsepower. Using the same math, to get 50 horsepower with an 1800 pound weight, you would need it to be descending at 15.3 feet per second (so you could only get 50hp for a very short time unless you have an extremely long distance for the weight to descend).

I think everyone is missing my concept here, just imagine a block and tackle but in reverse, same principal. it would takes less weight to move my gear reduction (series of 3 or 4)

256bits
Gold Member
I think everyone is missing my concept here, just imagine a block and tackle but in reverse, same principal. it would takes less weight to move my gear reduction (series of 3 or 4)

sorry but no.
You need 50hp in to get 50hp out, assuming no friction losses over you pulley system.
Gears or pulleys change the torque and angular velocity from input to ouput but not the hp.

Thanks 256bits! ok that makes sense but somehow i just can't comprehend the 7600 lbs needed that would be pulling down by gravity on the pulley to obtain my 50hp. to me as a layman it just seems a bit much. To me it seems the the torgue would increase by the use of the gear reduction right? Meaning One would need less weight correct me if im wrong

cjl
Thanks 256bits! ok that makes sense but somehow i just can't comprehend the 7600 lbs needed that would be pulling down by gravity on the pulley to obtain my 50hp. to me as a layman it just seems a bit much. To me it seems the the torgue would increase by the use of the gear reduction right? Meaning One would need less weight correct me if im wrong

You keep overlooking the fact that the weight will depend on the velocity at which the weight is descending (which is how it is related to the gear reduction). The fact that you want your output to be much faster than your input actually increases the weight required though, since increasing the output speed (relative to the input) will decrease the output torque. You could (in theory) obtain the 50hp with a one-pound mass, but it would need to be falling at a bit over 5.2 miles per second (which is clearly not reasonable).

ok i have 8ft of room to work with here lets say. That is the vertical length of the drop of the weight that I would want to take (hypothetcally speaking) 1 hr to fall in that 8 ft vertical span. And having the gear reducers set up for it to perform in that matter. So in your calculations you say the more time i need for the drop to occur, the more weight I need? I think that at some point you will reach an equilibrium where the amount of weight doesn't matter it will just drop and spin everything out of control. So with that being said how much weight would I need to perform this experiment under these conditions? This is a planned experiment so I need some accurate answers. But I am going to start with my calculated 1800lbs if i need more weight, i will add more. I will keep everyone updated on this one.

cjl
8 feet in an hour? That's only 0.67 mm/s, so you'll need an enormous weight (~5600 metric tons, if my calculations are correct, or a cube of solid lead about 8 meters on a side...)

QuantumPion
Gold Member
8 feet in an hour? That's only 0.67 mm/s, so you'll need an enormous weight (~5600 metric tons, if my calculations are correct, or a cube of solid lead about 8 meters on a side...)

This crane could lift it. It uses 5 diesel generators totaling 3500 hp to do so though. Also I doubt you'd be able to fit it in a room with an 8 ft ceiling :)

russ_watters
Mentor
ok i have 8ft of room to work with here lets say. That is the vertical length of the drop of the weight that I would want to take (hypothetcally speaking) 1 hr to fall in that 8 ft vertical span. And having the gear reducers set up for it to perform in that matter. So in your calculations you say the more time i need for the drop to occur, the more weight I need? I think that at some point you will reach an equilibrium where the amount of weight doesn't matter it will just drop and spin everything out of control. So with that being said how much weight would I need to perform this experiment under these conditions? This is a planned experiment so I need some accurate answers. But I am going to start with my calculated 1800lbs if i need more weight, i will add more. I will keep everyone updated on this one.
I think you need to slow down, read thoroughly, and absorb what is being explained to you. Three keys here:

1. You need to understand the difference between power and energy and how to calculate them. The equations are simple.
2. You need to recognize that conservation of energy applies to gears, so gearing is irrelevant to the energy/power calc.
3. But if you want to think about gearing, you need to learn that a reducing gear DECREASES the RPM. You are not dealing with a reducing gear.

We get this same question about once a month and the intuition of the poster is always very wrong.

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russ_watters
Mentor
By the way, it turns out this is an easy calc to keep English, so I'd do that. 1 HP is 550 ft-lb/sec, so 50 HP for an hour, up 8 feet is
50*550*3600/2000/8=6188 tons