I was at the gun range shooting my .50 BMG today. I know its quoted at 12,000 ft lbs but was thinking how many HP that was. I did some figuring than my brain started hurting. I asked an engineer on  Biggerhammer.com   This is his responce....


Let's assume that the projectile possesses the oft-quoted 12,000 ft-lbs of energy. One horsepower is defined as 550 ft-lbs/second according to my Funk & Wagnall's.

Now, further let's assume an exit muzzle velocity of 2,700 fps and a barrel length of 31 inches. I shall do a VERY sloppy calculation here, and assume that the projectile travels 2700 FPS for the entire length of the barrel, which is obviously wrong.

The time the projectile spends in the barrel is ( 1 )/( 2700fps /(12in/ft)*31" ), or 0.00096 seconds. (I will downgrade this to about 0.002 seconds because the average velocity "down the barrel" is NOT 2700 fps. Today I am lazy so I shall not calculate a better value... Heck, I am a mechanical engineer but nonetheless lazy. Heh heh...)

In that 0.00096 seconds we have imparted 12,000 ft-lbs of energy into the projectile. Thus we have exerted a power of (12000ft-lbs/.002 sec) = 6,000,000 ft-lbs/sec.

In horsepower, this equates to (12,541,000 / 550) = ~ 10,909 horsepower. AWESOME!!!!

However let us examine this bodacious amount of power:

1. It is only expended for about one-thousandth of a second.

2. Even MORE power is expended, because I have not accounted for energy expended in pushing a projectile (against its frictional will) down a rifled barrel that is slightly smaller inside than a projectile is outside. I have also not accounted for the power expended in recoiling the rifle, or the power expended in muzzule blast, etc...

3. My guess is true horsepower expended in the VERY small amount of time is probably approaching 15,000 or so.

Just think how much power is ABSORBED when a 50 BMG projectile impacts its target at close range. The time of absorption is HUGELY less than the 0.002 seconds quoted above.

A 3.5" thick manhole cover does not stand a chance. :-)

I may be taking a simplistic view of this – afterall, converting a firearm's energy to horespower is not something I do all the time.

If the exit mussle velocity is 2,700ft/sec and your projectile weighs 1 lb, it seems to me you would have 2,700ft.lbs/sec (about 5 h.p.).

If your projectile wieghs 1 oz, you'd have 0.3 h.p.

My figures are a lot less than the 11,000 h.p. you suggest, but, would you really want to shoot something with a kick like 11,000 horses?

Hey Im not sure either. I think his formula takes into account ACCELERATIG a mass of 750 grains  from "0" to "2700 feet per second" with an exit energy of 12,000 Ft lbs in a very short amount of time.  Hp is basicly force x time.

Where the hell are you going to find A 3.5 inch thick manhole cover, if such a thing existed do you know how much it would weigh?

That would give John Force a run for the money.

Fourteen hundred and ninety-two Columbus sailed the ocean blue. Cut the son of a bitch in two and that's how many watts are in a horsepower.

By my calculations based upon your 10,909 HP, your .50BMG exerts 8,138,114 watts.

Maybe I should start using gunpowder to power my house instead of buying electricity from the electric company! [:)]

Yeah, that 3.5" manhole cover thing is bogus. If you watch that Marine Corps training video where they talk about the cover, you notice that the cover isn't that thick, just the rim around the edges. No way in hell a .50 BMG will zip through 3.5" of steel. If it could, we wouldn't be buying all those M1's would we =)

Power is the amount of work done per unit time or the time rate of doing work (using energy).

Power*time units) 1hp= 550ft-lbs/s= 746W  
one gr (grain) = .65 g
one oz (ounce) = 28.35 g

M33 50BMG
Bullet = 649gr = 421g = .93002lb
Muzzle Energy = 12,200ft-lbs
Muzzle Velocity = 2910ft/s (36" barrel)
Ballistic coefficient = .65
Max range 2,000-3,000 yds

Lets look at the WORK PERFORMED to get a 50 cal bullet to max effective range.
Estimations:
AVG V to 9000ft = 2425ft/sec
AVG E to 9000ft = 9100ft-lbs


Time = AVG V = 2425ft/sec for 9000ft.           = 3.711sec

9,100ft-lbs/3.711sec =  Power or Energy of projectile
2452ft-lbs/sec
Conversion: 1HP = 550ft-lbs/s

= 4.49HP

OR (.93lb mass of bullet) *(9000ft distance) /(3.71sec time) = 2256ft-lb/sec = 4.10HP  


Differences are due to fudged avg V and E numbers.

I had a second person go over it  and his result were very simular, see below.....


I did it in the SI metric system, since I’m more comfortable in it. I seem to be getting results very similar to yours (surprise). Please note, however, that when typing your results for the time that it takes the bullet to travel the barrel length, you missed a “1” – you wrote 0.00096 seconds, whereas you meant to write 0.00196 seconds. In any event, you rounded it off to 0.002 seconds (so it was obviously merely a typo.)

Power = Energy / time

1. Time it takes to traverse the barrel-length:

V (the barrel exit velocity) x time / 2 = barrel length i.e., vt/2 = s

Assuming 31” barrel (0.787 meter) and final velocity of 2700ft/sec (823 m/sec), the time to traverse the barrel is 0.0019 seconds

2. The energy 12,000 ft-lb translates into 16256 Joules
(using 1 ft = 0.3048 meters and 1 lb = 0.225 Newton)

3. Hence, power E/t = about 8.5 million Watts, or 11,300 HP (using 1HP = 746 watts)

Now, of course this lasts only for 1.9 milliseconds, as you pointed out (and the amount of energy is not astronomical.)

Let’s see… enough energy to raise the temperature of 1 quart of water by about 15 degrees Fahrenheit.

OK, this high-school physics was fun. Thanks for your input

I think that what you have seen from my own primitive calculations, based simply of mussle velocity x mass, and the more sophisticated calculations of others, that you do not possess a 11,000 h.p. firearm.

If you did, every (make that only) time you pulled the trigger, you would wind up about 200m further away from the target than you started from – waiting for the ambulance to arrive.

My Drag Car tipped the scales at 3080 Lbs with me in it...

It ran a 1/4 mile (1320ft) in 8.46 seconds at 159.85 MPH...

It covered the first 60 feet in 1.21 seconds...


Put that in your pipe & smoke it...
[:D]

There's no friggin way you have 10,000 HP coming out of your .50's gun barrel...

Damn Art! By my calculations your racecar has over 560,000 horsepower! You must be a race winning son of a gun!! [:)]

Where do I buy that rifle????
[:D]

Gunman0,
More to the point, how do I get that horsepower in my '74 Vega?

First off I was just QUOTING the reports from two engineers. These are not my calculations.

In responce two a couple answers.

1) first stcyr, You state that if I had this amount of HP I would send me flying BUT the published reports state the muzzle energy from a standard ball .50 BMG round is 12,000 FT lbs. Why isnt this destroying my shoulder???

2) Boomholzer, Are you calculating accelerating this mass form "0" to "2900 ft per second" in this short amount of time (.002 seconds)? It looks like your formulas is just stating the energy needed for  the projectile to cover this distance while its already in motion. ?

3)Drager art
[img]http://us.f1.yahoofs.com/users/a5e4c29d/bc/My+Photos/__hr_nova+motor---1.jpg?bc_POA9AsliGOiom[/img]

This is my STREET ride , a high 9 second N2O injected big block 2800 lb Nova so Im not new to HP vs FTlbs. No its not a 8 second strip ride but I have a basic understandingof how this work. These engines are producing 700 hp over a LONG time (8-9 seconds) comaperd to the .002 seconds we are talking here. Time is the big differnace in these equations.


Lastly im trying to figure HOW MUCH ENERGY ( HP)needed to ACCELERATE a .750 gr weight from 0 to 2800 ft per sec in .002 seconds to get the claimed 12,000 ft lbs of energy???

My under standing ( hey Im just learning) that this much energy is only available for a  short amount of time (.002 seconds) agaisnt a very small object. Hey 10,909 HP sound like alot to me too.. but so does 12,000 ft lbs. quoted.

Very nice motor Mr. Nova [:D]

I forgot to menton, my car was also in street trim with Big Block & 'glide w/nitrous...

'70 Camaro...515 BBC(4.392 x 4.250), Brodix -2+ heads, 14.5-1 JE's, +.250 Manley H-beams, Callies 4340 crank, Comp Cams roller 286/298 @.050 /.748/.748 lift, Jesel belt drive, 1250cfm Dominator, NOS Big Shot plate system, M/T ET Streets, and 4" Flowmasters...

Car went an average of mid 9.50's @ 140-142 OFF the bottle, and 8.40's @ 156-159+ ON the bottle...

60ft times were mid 1.30's OFF the bottle, and low 1.20's ON the bottle...

Car was ALWAYS street legal...
Never ran it without exhaust or street tires...

Car would have gone 8.20's or 8.30's on the fogger system...

I was forced to sell the car back in November after my Dad died suddenly...
Had to help support my Mom, Dad had no life insurance...

Of course since I'm married w/4 kids, I'll NEVER be able to afford to build another one like it, unless I hit the lotto...

If I hit the lotto, I'll be buying machineguns instead of race cars though [:D]

Guns are my new hobby...


Glad to see somebody actually had the balls to stuff a BBC in a little '65 deuce [:D]
Usually I only see SBC's in them....
Good job !!

I'll see if I can find a pic of my motor to send 'ya...

Racer, sorry to hear of your loss. You have to put family before any hobby.I could only afford to start playing again because my children are finally on their own and I divorced.

To tell the truth I not going to build anymore cars either,Not wild ones anyway. Too much money involved. I only built this one because I had the parts left over from my younger days when you could buy big block stuff for nothing. Its a  433 with GMPP heads, 2.25/1.88 valves ,comp cams valve train, muncie tranny ( love to bang gears) and a 9 inch with a locker. I waiting for the tranny to let lose some day. Just your basic race car stuff stuck on a street car.

[img]http://us.f1.yahoofs.com/users/a5e4c29d/bc/My+Photos/__hr_chevy+vs+ford+2.jpg?bc_POA9Aa6Od1GNU[/img]

Now Im getting into the fire arms game too after many years. Had a SP1 years ago and sold it for $250 before the big pre ban shit hit the fan.

I bought the .50 aboout a year ago and enjoy it but I not real good with math so thats why Im asking around about these energy issues. I dont know how to figure it and wanted to run these engineers forumlas by everybody.

Im building a RRA AR-15 right now as funds come along. 2stage trigger, non collasable a4 stock ( to keep it legal) and a 18" varmit front end.

Just a helpfull bit of advice...

Go to an electric water pump and fan, they are VERY streetable (CSI is a real good pump)

Use the NOS "Big Shot" plate, instead of the "Cheater" plate...
Big gains there...
Get rid of the "Pro-shot" NOS solenoid, and replace it with the bottom exit, blue "race" solenoid...
You WILL pickup 2+ tenths EASY...
Be sure to crank up the fuel pressue with the new solenoid, it uses ALOT of fuel...
Start out at 7.5 lbs, and don't go under 6.5 lbs, It'll go lean on you under 6.5 lbs....
I assume your using the MSD 7AL-2 Ignition with a crank trigger ?
If not, get one...
You will be amazed at how clean the car will idle & rev with a crank trigger...
Best $200 I ever spent...
Also, the MSD retard box is a must...
Pull out 12 degrees of timing when the juice comes on...

DON'T FORGET COLD SPARK PLUGS !!!
Autolite #2593 or #2594 worked best for me...

I strongly suggest a seperate dedicated fuel system for the Nitrous...
A 1 gallon cell up front works great...
The NOS system alone will use every bit of fuel a Holley blue pump can feed it...The "blue" pump is a bare minimum to feed it...

Another suggestion is to install a small bypass line (-04) just before the fuel solenoid...put a small NOS jet inline so you don't bleed off too much pressure (030-040)
The bypass line will return the air bubbles and warm fuel back to the 1 gallon cell, and stabalize your fuel pressure, eliminating the "pressure creep" while the pump is running...

I see you are using the Holley regulator on the nitrous side...
DON'T use anything but the Holley regulator...
For some reason the Holley regulator seems to work best...
I know alot of guys that burned up engines using the BG or Mallory regulators on the NOS side...

If your car is running 9.50's, it should EASILY be able to squeak into the 8's...
From what I see in the picture, you have another 1/2 second you can get out of that car...

If you can't get that car into the 8's with my suggestions, I will "EAT MY SHORTS" [:D]

I've got a buddy running one of my 454's in a 3300lb '64 Chevelle right now...
He went a 9.54 @ 148mph in street trim spinning the tires...
60ft's were nasty...1.60's [:D]

You will need to go 150 MPH if you want to hit the 8's...
Should be easy with that little 2800lb Nova...

I believe that x lbf ft (not ft lb) is the unit used to measure how much force is needed to move an object with a mass of xlb 1 foot (or 10xlb 0.1 ft, 0.1xlb 10x feet, etc.) 100 lbf ft would move a 1lb object 100 feet, a 10lb object 10 feet, or a 0.1lb object 1000 feet. 1 oz = +/- 437 grains, so the M33 ball mentioned above has a mass of approximately 1.5oz or 0.1lb. Therefore, the projectile should travel 120,000 feet when acted on by a force of 12,000 lbf ft - but that doesn't take into consideration factors such as friction in the barrel, air resistance, or gravity. Assuming your body has a mass of 200lb, the 12,000 lbf ft would impart a peak force of 60lb to your shoulder, but that's moderated by the recoil system, mass of the gun, any muzzle brake, your body not being free-floating in space (i.e. friction with the ground), your body moving with the recoil force, etc. It works much the same way as hydraulic pressure, I guess - a force of 10Kpsi acting on a square surface measuring 2" per side would produce 40Klb of force because F=PA, and the same force acting on a square surface measuring 0.5" per side would produce only 2500lb force.

At least, that's how I see it - I failed high school physics though! [:D]

Edited to change some of my math

Dragracer art was kind enough to send a picture  of his late pride and joy but was not able to post it. So here it is, One Bad Camaro !!!



[img]http://us.f1.yahoofs.com/users/a5e4c29d/bc/My+Photos/__hr_snapshot.jpg?bc_POA9A73iy2Mfw[/img]

Thanks for posting the pic for me...

Unfortunately, 99.9% of my pictures were given to the guy that bought my car...
I asked him to pick through them, and send back the ones he didn't want...

I guess he wanted all of them, I never got any back from him...

Car & pics went to Fairbanks, AK...
I'll never see the pics again I'm sure...

'Kinda pisses me off a little...
O-well...

Thanks again Mike for posting my pic [:D]

you cant convert horse power to foot pounds.

foot pounds measures kinetic energy which is mass times the square of the velocity

horsepower measures power, which is a rate, and therefore has a dimension of time involved.

the two are not interchangeable.

it is like trying to measure how long it took you to cook your breakfast in meters.

it no compute

-Spaceman

SpacemanSpiff,

I suspect that Hobbs must have clued you in to the irrationality of this thread and made you post. But thanks anyway, you cleared away some of the cobwebs that had hindered my response.

Horsepower vs muzzle velocity ect? Don't like to admit it, but I got sucked in!