Age old question... torque vrs horsepower
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Checked the trig textbook, and found no reference to "rad" as an imaginary unit. Ditto for the physics textbooks.
If you claim rads are not a true engineering unit, I won't argue as I have little expertise in that field. In physics though, the rad is considered a real unit which can be visually represented (draw an arc where the radius and the subtended arc length are equal) and measured. Hopefully, you are not saying that engineering does not rely on a knowledge of fundamental physics.
'Radian' angles are a ratio or arclength over radius where the units clearly cancel each other out.
I'll agree that the units on one side of the equation cancel each other out, but to make the equation work you need to insert units on both sides.
For instance if we have an arc of unknown rad, with a radius of 1 m and a subtended arc length of 2 m, then we would subtitute this information into the formula and calculate:
Q = s/r
rad = 2 m/1 m
rad = 2/1
rad = 2
If you claim rads are not a true engineering unit, I won't argue as I have little expertise in that field. In physics though, the rad is considered a real unit which can be visually represented (draw an arc where the radius and the subtended arc length are equal) and measured. Hopefully, you are not saying that engineering does not rely on a knowledge of fundamental physics.
'Radian' angles are a ratio or arclength over radius where the units clearly cancel each other out.
I'll agree that the units on one side of the equation cancel each other out, but to make the equation work you need to insert units on both sides.
For instance if we have an arc of unknown rad, with a radius of 1 m and a subtended arc length of 2 m, then we would subtitute this information into the formula and calculate:
Q = s/r
rad = 2 m/1 m
rad = 2/1
rad = 2
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From: PA
Originally posted by ZWILD1
Q = s/r
rad = 2 m/1 m
rad = 2/1
rad = 2
Q = s/r
rad = 2 m/1 m
rad = 2/1
rad = 2
In your example i would say that
Theta=2
and if you wish,
Theta = 2 (rad)
My intent was not to start a crusade against the radian. Many people do use this term. It is useful when teaching people geometry because many for many people the concept of an angle being represented by simply a number is unsettling.
Look at it this way.
Radians is a label given to a number, to specify that number represents the ratio of arclength over radius. It is a label, not a unit. Degrees is also a psuedo-unit.
Are you familiar with dimensional analysis? It is a very useful tool and important concept in engineering and physics alike. Dimensional Analysis requires you follow the rules of "fundemental units".
Here are the SI base units, or fundemental units.
length meter m
mass kilogram kg
time second s
electric current ampere A
thermodynamic temperature kelvin K
amount of substance mole mol
luminous intensity candela cd
All other 'units', like HP, are derived units, or combinations of the above fundemental units.
Notice Radians is not listed as a Fundemental Unit or SI Base Unit. You are using the laymans meaning of the word 'unit' and to me the word 'unit' implies that we are talking about Engineering Units or Fundemental Units which are required when talking about dimensional analysis.
How do you answer the original question then?
I said the expression is
tq*rpm/5252 = HP which has the units (lb*ft/min) just like the definition of 1 hp = 33,000 ft*lbs/min
According to your 'units'
HP = (ft*lbs*rad/min)
because 33,000/2pi(rad)=5252(rad^1) or units of (1/rad).
What are you going to do to cancel out the radians? How do you handle that situation?
I admit that in my quick google I couldn't find a good link relevent to the specifics of the radian. There are many mentions of it on the web, but not many (any that i could find) which address the specifics of it in the context of this discussion.
I'm not the best person at explaining these things. Will someone help me out here. I know there are people who understand where i am coming from. (ahem....Jon, Bret, Rich)
BTW, i just won 3rd place at the Penn State Mechanical Engineering Senior Design Competition, this is my educational background. I'm not just trying to blow smoke up your *** or argue for the sake of argueing.
Off too happy hour (working that is).
-brent
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Posts: 1,591
From: PA
A radian is a dimensionless quantity. 2pi, the number of 'radians' in a circle is a naturally occuring number.
Check out this article on dimensional analysis.
I should have just thrown 2pi in the original post and skipped the 'radian' all together
I thought that might cause confusion as well though.
-brent
Check out this article on dimensional analysis.
I should have just thrown 2pi in the original post and skipped the 'radian' all together
I thought that might cause confusion as well though. -brent
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Posts: 2,370
From: Germany
Originally posted by OldSStroker
... If you measured it running up stairs, torque would be hard to figure.
... If you measured it running up stairs, torque would be hard to figure.
and yes i got my quote from oldSStroker
units is a poor way to describe radians... my father is a calculus teacher... personally i would call it a system of measuring just like english or metric. its a system of measuring a degree of a circle.
inches and feet are units... but i wouldnt call radiants a unit... ohh well, dictionary.com says its considered a unit....
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From: Upstate NY
I like radians for a different reason.
A radian is about 57.3 degrees (360/2PI), and many vehicles have a wheel track of just about 57 degrees, so a 1 inch change equals one degree for all practical purposes.
After I read about your .6 hp test, I finally got my Schwinn Air-Dyne up to 85 rpm in an all out burst after lots of warm up. According to Schwinn, that's .658 hp. Of course I was using arms and legs both. FWIW, that was also 490.3 watts or 3000 Kilopond meters per minute (a much less familiar measure of power). At 85 rpm I was able to generate 40.65 lb-ft. at the pedals...but not for long, as my volumetric efficiency isn't very good there. Probably 60-65 pedal rpm is much more efficient. That's where I "cruise" at about .26 hp.
Oh yeah, conditions were very close to SAE 60* F, so I'll call it a corrected hp.
More than you ever wanted to know!
A radian is about 57.3 degrees (360/2PI), and many vehicles have a wheel track of just about 57 degrees, so a 1 inch change equals one degree for all practical purposes.
After I read about your .6 hp test, I finally got my Schwinn Air-Dyne up to 85 rpm in an all out burst after lots of warm up. According to Schwinn, that's .658 hp. Of course I was using arms and legs both. FWIW, that was also 490.3 watts or 3000 Kilopond meters per minute (a much less familiar measure of power). At 85 rpm I was able to generate 40.65 lb-ft. at the pedals...but not for long, as my volumetric efficiency isn't very good there. Probably 60-65 pedal rpm is much more efficient. That's where I "cruise" at about .26 hp.
Oh yeah, conditions were very close to SAE 60* F, so I'll call it a corrected hp.
More than you ever wanted to know!
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Joined: Apr 2003
Posts: 1,591
From: PA
Now this topic is getting interesting
I used to race at the lehigh valley velodrome. Most competitive cyclists consider a steady state 70-100 rpm cadence to be ideal. Track cyclist favoring the high end and road cyclists the low end.
I'm sure there are calibration differences between the big fanned aerodyne and the the cateye trainers that we were using. Also, you use a 160-170 mm crank, 165 being most common, on the track versus the 172.5 or 175 of a road bike and that obviously makes a difference in peak rpm.
When i was competitive around 16 I put out close to 1200 watts on a cateye1000 cycling trainer in a standard 10 second 81" gear test. That was nearing 150 rpm. With the cateye you could definitly turn an even higher wattage by using another gear but using the 81" gear was the standard for comparison. Most of the professional where in the 1300s and top pro's such as Marty Nothstein the world champion match sprinter and olympic medalist were around 1450w. The difference between cyclist becomes MUCH more apparent if you switch to a 20 second test.
Of course now days i am probably WAY down on power since i only go for a road ride about once a year with my dad.
-brent
I used to race at the lehigh valley velodrome. Most competitive cyclists consider a steady state 70-100 rpm cadence to be ideal. Track cyclist favoring the high end and road cyclists the low end.
I'm sure there are calibration differences between the big fanned aerodyne and the the cateye trainers that we were using. Also, you use a 160-170 mm crank, 165 being most common, on the track versus the 172.5 or 175 of a road bike and that obviously makes a difference in peak rpm.
When i was competitive around 16 I put out close to 1200 watts on a cateye1000 cycling trainer in a standard 10 second 81" gear test. That was nearing 150 rpm. With the cateye you could definitly turn an even higher wattage by using another gear but using the 81" gear was the standard for comparison. Most of the professional where in the 1300s and top pro's such as Marty Nothstein the world champion match sprinter and olympic medalist were around 1450w. The difference between cyclist becomes MUCH more apparent if you switch to a 20 second test.
Of course now days i am probably WAY down on power since i only go for a road ride about once a year with my dad.
-brent
Last edited by 94formulabz; Dec 13, 2003 at 11:02 PM.
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From: Germany
well i did a little reaserch with my dad and 1 hp = 550ft/lbs per second
so if my engine does 325 ft/lbs stock (lt1)
at 2400 rpm's... 40 times per second...40*325=13000... 13000/550... ive got 23 horsepower
musta done some bad research...
ok here this makes sense i didnt intigrate angles...
"But engine speed is normally referred to in revolutions per minute (RPM). Since we want a "per second," we need to convert RPMs to "something per second." The seconds are easy -- we just divide by 60 to get from minutes to seconds. Now what we need is a dimensionless unit for revolutions: a radian. A radian is actually a ratio of the length of an arc divided by the length of a radius, so the units of length cancel out and you're left with a dimensionless measure.
You can think of a revolution as a measurement of an angle. One revolution is 360 degrees of a circle. Since the circumference of a circle is (2 x pi x radius), there are 2-pi radians in a revolution. To convert revolutions per minute to radians per second, you multiply RPM by (2-pi/60), which equals 0.10472 radians per second. This gives us the "per second" we need to calculate horsepower.
Let's put this all together. We need to get to horsepower, which is 550 foot-pounds per second, using torque (pound-feet) and engine speed (RPM). If we divide the 550 foot-pounds by the 0.10472 radians per second (engine speed), we get 550/0.10472, which equals 5,252. "
so if my engine does 325 ft/lbs stock (lt1)
at 2400 rpm's... 40 times per second...40*325=13000... 13000/550... ive got 23 horsepower
musta done some bad research...
ok here this makes sense i didnt intigrate angles...
"But engine speed is normally referred to in revolutions per minute (RPM). Since we want a "per second," we need to convert RPMs to "something per second." The seconds are easy -- we just divide by 60 to get from minutes to seconds. Now what we need is a dimensionless unit for revolutions: a radian. A radian is actually a ratio of the length of an arc divided by the length of a radius, so the units of length cancel out and you're left with a dimensionless measure.
You can think of a revolution as a measurement of an angle. One revolution is 360 degrees of a circle. Since the circumference of a circle is (2 x pi x radius), there are 2-pi radians in a revolution. To convert revolutions per minute to radians per second, you multiply RPM by (2-pi/60), which equals 0.10472 radians per second. This gives us the "per second" we need to calculate horsepower.
Let's put this all together. We need to get to horsepower, which is 550 foot-pounds per second, using torque (pound-feet) and engine speed (RPM). If we divide the 550 foot-pounds by the 0.10472 radians per second (engine speed), we get 550/0.10472, which equals 5,252. "
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From: Upstate NY
Originally posted by 94formulabz
Now this topic is getting interesting
I used to race at the lehigh valley velodrome. Most competitive cyclists consider a steady state 70-100 rpm cadence to be ideal. Track cyclist favoring the high end and road cyclists the low end.
I'm sure there are calibration differences between the big fanned aerodyne and the the cateye trainers that we were using. Also, you use a 160-170 mm crank, 165 being most common, on the track versus the 172.5 or 175 of a road bike and that obviously makes a difference in peak rpm.
When i was competitive around 16 I put out close to 1200 watts on a cateye1000 cycling trainer in a standard 10 second 81" gear test. That was nearing 150 rpm. 39x15 tooth sprocket and cog with 700mm diameter rim+tire equals ~80.5-81 inches or forward motion per crank revolution. With the cateye you could definitly turn an even higher wattage by using another gear but using the 81" gear was the standard for comparison. Most of the professional where in the 1300s and top pro's such as Marty Nothstein the world champion match sprinter and olympic medalist were around 1450w. The difference between cyclist becomes MUCH more apparent if you switch to a 20 second test.
Of course now days i am probably WAY down on power since i only go for a road ride about once a year with my dad.
-brent
Now this topic is getting interesting
I used to race at the lehigh valley velodrome. Most competitive cyclists consider a steady state 70-100 rpm cadence to be ideal. Track cyclist favoring the high end and road cyclists the low end.
I'm sure there are calibration differences between the big fanned aerodyne and the the cateye trainers that we were using. Also, you use a 160-170 mm crank, 165 being most common, on the track versus the 172.5 or 175 of a road bike and that obviously makes a difference in peak rpm.
When i was competitive around 16 I put out close to 1200 watts on a cateye1000 cycling trainer in a standard 10 second 81" gear test. That was nearing 150 rpm. 39x15 tooth sprocket and cog with 700mm diameter rim+tire equals ~80.5-81 inches or forward motion per crank revolution. With the cateye you could definitly turn an even higher wattage by using another gear but using the 81" gear was the standard for comparison. Most of the professional where in the 1300s and top pro's such as Marty Nothstein the world champion match sprinter and olympic medalist were around 1450w. The difference between cyclist becomes MUCH more apparent if you switch to a 20 second test.
Of course now days i am probably WAY down on power since i only go for a road ride about once a year with my dad.
-brent
Wow! 1200 watts is 1.6 hp and 1450 is almost 2 hp! At 150 rpm that's over 56 ft-lb. I hope you are way down on power now.
Of course, I'm probably older than your dad, but I was never much better on a bike because I didn't ride much. I do it now for muscle tone, especially the cardiac muscle. I don't do .6 hp very often.With the 10 second or 20 second test that's sorta like a drag race. If you ran a ProStock engine anywhere near peak power for much more than it's sub 7 second runs, it probably would gernade. At 150 pedal rpm and 1200+ watts you propbably would also!
When Bryan Allen powered the Gossamer Condor human powered aircraft for about 7-1/2 minutes to win the Kremer Prize he averaged about 1/3 hp or 250 watts. Paul MacCready used .4 hp as what a cyclist like Allen could put out continuously (as an endurance engine).
I've read that Lance Armstrong can sustain .5 to .6 hp for an hour under ideal conditions. Whew!
It's amazing to me how efficient a bicycle can be. To move over 160 lbs. at maybe 25 mph with about .4 hp. That equates to about 9 hp to move a Camaro that fast on level ground. 3 or 4 times that might be closer. Bicycling is way more efficient than walking or horseback riding or flying. The passenger is the powerplant, and he/she gets health benefits from the riding.
Perhaps it's significant that the Wright Brothers were bicycle guys before they flew (100 years ago next Wednesday).
My $.02
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From: Germany
Originally posted by OldSStroker
Wow! 1200 watts is 1.6 hp and 1450 is almost 2 hp! At 150 rpm that's over 56 ft-lb. I hope you are way down on power now. Of course, I'm probably older than your dad, but I was never much better on a bike because I didn't ride much. I do it now for muscle tone, especially the cardiac muscle. I don't do .6 hp very often.
With the 10 second or 20 second test that's sorta like a drag race. If you ran a ProStock engine anywhere near peak power for much more than it's sub 7 second runs, it probably would gernade. At 150 pedal rpm and 1200+ watts you propbably would also!
When Bryan Allen powered the Gossamer Condor human powered aircraft for about 7-1/2 minutes to win the Kremer Prize he averaged about 1/3 hp or 250 watts. Paul MacCready used .4 hp as what a cyclist like Allen could put out continuously (as an endurance engine).
I've read that Lance Armstrong can sustain .5 to .6 hp for an hour under ideal conditions. Whew!
It's amazing to me how efficient a bicycle can be. To move over 160 lbs. at maybe 25 mph with about .4 hp. That equates to about 9 hp to move a Camaro that fast on level ground. 3 or 4 times that might be closer. Bicycling is way more efficient than walking or horseback riding or flying. The passenger is the powerplant, and he/she gets health benefits from the riding.
Perhaps it's significant that the Wright Brothers were bicycle guys before they flew (100 years ago next Wednesday).
My $.02
Wow! 1200 watts is 1.6 hp and 1450 is almost 2 hp! At 150 rpm that's over 56 ft-lb. I hope you are way down on power now.
Of course, I'm probably older than your dad, but I was never much better on a bike because I didn't ride much. I do it now for muscle tone, especially the cardiac muscle. I don't do .6 hp very often.With the 10 second or 20 second test that's sorta like a drag race. If you ran a ProStock engine anywhere near peak power for much more than it's sub 7 second runs, it probably would gernade. At 150 pedal rpm and 1200+ watts you propbably would also!
When Bryan Allen powered the Gossamer Condor human powered aircraft for about 7-1/2 minutes to win the Kremer Prize he averaged about 1/3 hp or 250 watts. Paul MacCready used .4 hp as what a cyclist like Allen could put out continuously (as an endurance engine).
I've read that Lance Armstrong can sustain .5 to .6 hp for an hour under ideal conditions. Whew!
It's amazing to me how efficient a bicycle can be. To move over 160 lbs. at maybe 25 mph with about .4 hp. That equates to about 9 hp to move a Camaro that fast on level ground. 3 or 4 times that might be closer. Bicycling is way more efficient than walking or horseback riding or flying. The passenger is the powerplant, and he/she gets health benefits from the riding.
Perhaps it's significant that the Wright Brothers were bicycle guys before they flew (100 years ago next Wednesday).
My $.02
i mean could u imagine if u could race the entire 1/4 mile running at peak horsepower?
ur time would be considerably lower.
but
a big rig w/ not to much more power then our engine has. maybe 400 hp and 600 tq or so...
my boss just weighed in his tractor & trailer (86 peterbuild) at 80,500 lbs. and continued to roll down the hill... with those trucks can have 8-16 gears... while an average bike has 21 or like my dads bike (he road to boston from LA 3000+ miles) has 28 i think.
if our engines peaked at 40-60ft-lbs at 90-150 rpms... thats a lot more power then i think or engines put out. but i donno if u can compare them.
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From: Upstate NY
Originally posted by NewbieWar
well uve got to take into consideration gearing is what makes a bycicle efficent, during the last few months ive been trying to design a transmission w/o gears... with little knowledge about transmissions its taking me a while
i mean could u imagine if u could race the entire 1/4 mile running at peak horsepower?
ur time would be considerably lower.
Well, perhaps. CVT or continuously variable transmissions are available in some cars and they aren't that much quicker. Your typical snowmobile does exactly as you said.
How about a Top Fuel or Funny Car. Idle to 8000 (which it holds throughout the run) in a couple tenths of a second, then the clutch lets the car catch up as the tires grow in diameter to vary the 'transmission' ratio. Now that's strange. Boy are they quick!
It isn't just gearing in a bicycle that makes it efficient. Low vehicle weight, very low rolling resistance, and a very efficient driveline, as well as the bit about the payload being the powerplant help a lot.
but
a big rig w/ not to much more power then our engine has. maybe 400 hp and 600 tq or so...
my boss just weighed in his tractor & trailer (86 peterbuild) at 80,500 lbs. and continued to roll down the hill... with those trucks can have 8-16 gears... while an average bike has 21 or like my dads bike (he road to boston from LA 3000+ miles) has 28 i think.
if our engines peaked at 40-60ft-lbs at 90-150 rpms... thats a lot more power then i think or engines put out. but i donno if u can compare them.
Remember that those OTR diesel truck engines have that power at almost any rpm they run. For example, the 400 hp diesel at 1500 rpm has 1400 lb-ft of torque. If it only had 600 lb-ft @ 400 hp, that would be about 3500 rpm. I doubt they ever run that fast. (400*5252/600=3501). They have a limited rpm band of probably less than 1000 rpm, so lots of gears are necessary to go from 0 to maybe 85+ mph. I was passed by a rig when I was over 85 while trying to go thru Texas the long way in one day.
well uve got to take into consideration gearing is what makes a bycicle efficent, during the last few months ive been trying to design a transmission w/o gears... with little knowledge about transmissions its taking me a while
i mean could u imagine if u could race the entire 1/4 mile running at peak horsepower?
ur time would be considerably lower.
Well, perhaps. CVT or continuously variable transmissions are available in some cars and they aren't that much quicker. Your typical snowmobile does exactly as you said.
How about a Top Fuel or Funny Car. Idle to 8000 (which it holds throughout the run) in a couple tenths of a second, then the clutch lets the car catch up as the tires grow in diameter to vary the 'transmission' ratio. Now that's strange. Boy are they quick!
It isn't just gearing in a bicycle that makes it efficient. Low vehicle weight, very low rolling resistance, and a very efficient driveline, as well as the bit about the payload being the powerplant help a lot.
but
a big rig w/ not to much more power then our engine has. maybe 400 hp and 600 tq or so...
my boss just weighed in his tractor & trailer (86 peterbuild) at 80,500 lbs. and continued to roll down the hill... with those trucks can have 8-16 gears... while an average bike has 21 or like my dads bike (he road to boston from LA 3000+ miles) has 28 i think.
if our engines peaked at 40-60ft-lbs at 90-150 rpms... thats a lot more power then i think or engines put out. but i donno if u can compare them.
Remember that those OTR diesel truck engines have that power at almost any rpm they run. For example, the 400 hp diesel at 1500 rpm has 1400 lb-ft of torque. If it only had 600 lb-ft @ 400 hp, that would be about 3500 rpm. I doubt they ever run that fast. (400*5252/600=3501). They have a limited rpm band of probably less than 1000 rpm, so lots of gears are necessary to go from 0 to maybe 85+ mph. I was passed by a rig when I was over 85 while trying to go thru Texas the long way in one day.
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im unsure what we are arguing about... a bicycles pound per pound power... or gearing or torque or anything...
a bicycle is powered by a human body (the engine) 160lbs
bike... 30 lbs...
air... weightless for everything else theres mastercard (joking)
ok that makes for an engine 5.3 times heavier then the trasmission and wheels... donno how much an lt1 weighs... but perportionally its s.o.l. with a 3600 lbs car. probably weighing 200-300 lbs if the rest of the car was 56lbs... 9 hp would be sufficent... accually probably a bit much... but see how efficent a car is compared to a bike... put a roll cage some air bags a radio an airconditionor (gennerated by ur peddling) anti lock breaks a water pump (/w straw to mouth
... maybe some soda 
)
the list could go on... ur looking at 700 lbs or more!
that makes that bike very worthless... but now its a "safe bike" u wont get hurt and now uve got a few things that will make the ride more enjoyable... (probably a/c is more trouble then it adds)
still unsure what we are talking about tho...
.6 hp is good for a human body but it cant keep it up.
big rigs are powered about the same as a bike is... probably more so... 5000 lb engine to pull an 75,000 lb load with ease... heh he broke a spring on that last load...
hope it doesnt happen to often...
got an old double hay trailor 1961 i think...
a bicycle is powered by a human body (the engine) 160lbs
bike... 30 lbs...
air... weightless for everything else theres mastercard (joking)
ok that makes for an engine 5.3 times heavier then the trasmission and wheels... donno how much an lt1 weighs... but perportionally its s.o.l. with a 3600 lbs car. probably weighing 200-300 lbs if the rest of the car was 56lbs... 9 hp would be sufficent... accually probably a bit much... but see how efficent a car is compared to a bike... put a roll cage some air bags a radio an airconditionor (gennerated by ur peddling) anti lock breaks a water pump (/w straw to mouth
... maybe some soda )the list could go on... ur looking at 700 lbs or more!
that makes that bike very worthless... but now its a "safe bike" u wont get hurt and now uve got a few things that will make the ride more enjoyable... (probably a/c is more trouble then it adds)
still unsure what we are talking about tho...
.6 hp is good for a human body but it cant keep it up.
big rigs are powered about the same as a bike is... probably more so... 5000 lb engine to pull an 75,000 lb load with ease... heh he broke a spring on that last load...
hope it doesnt happen to often...got an old double hay trailor 1961 i think...
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From: Upstate NY
Originally posted by NewbieWar
im unsure what we are arguing about... a bicycles pound per pound power... or gearing or torque or anything...
im unsure what we are arguing about... a bicycles pound per pound power... or gearing or torque or anything...
Take efficiency of power transmission. A top ProStock driver, is said to be a fanatic about high efficiency and low power absorbtion in things like transmissions. In one case they were failing gears due to the huge loads thay take. They tried stronger teeth or more tooth contact, etc. The trans didn't break, but the car slowed down. That wasn't an acceptable solution. As ProStock power increases, as does traction/ tire technology and tire size, the weakest links go boom. The challenge is making the parts stronger and not lose any more power due to friction, deflection, etc. Oh yeah, and fix it before the season starts in a few weeks!
Keep thinking!
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