pounds and horsepower

[tzracer]

Brian I think I need an explaination of the horsepower determines acceleration theory. My understanding is that horsepower is a force X a distance over a time. This determines a terminal velocity (which by the way is more a function of drag than weight unless you are going uphill) As stated earlier the important factor in acceleration is torque.

I agree until the last sentance. Power is work/time. In a linear (non rotating) system work is force * distance. In a rotational system work = torque * angle (in radians, not degrees). Power is a combination of torque, angle and time. The angle and time are just as important as the torque. Sometimes it is written power = torque * angular velocity. The angular velocity is just as important as the torque when it comes to acceleration.

First let's agree that horsepower cannot be changed by gearing. Feel free to correct me if I am wrong here.

Second let's agree that torque CAN be changed by gearing. Again correct me if I am mistaken.

Looks ok.

Finally let's agree that ANY motorcycle accelerates better in 1st than it does in 5th.

IF you are at the same rpms. If you are at different rpms the bike may accelerate better in 5th than 1st (new R6, 1st gear at idle, compared to 5th gear just below the power peak).

In first gear the engines output, lets just grab a nice even number out of the air, 50 lbsft at 5000 RPM is converted by the transmission and sprocket ratio to 5000 lbsft at 50 rpm resulting in great acceleration but the engine exploding somewhere south of 50 mph (ok I guess by now you can tell I ride a twin, you modern inline guys substitute about 90 or so here). Now let's go to 5th gear and take that 50 lbsft at 5000 RPM and convert it to say 250 lbsft at 1000 RPM. Not nearly as much kick in the pants off the line but when your drag catches up with your ability to make horsepower (some amount of toque in some amount of time) you have a much better chance of being somewhere south of the point of engine explosion.

An interesting side note here is that peak horsepower is nearly always made at a higher RPM than peak torque. Reason being the relationship between speed and torque. As RPM increases the engine begins to have breathing problems and torque starts to fall off but since horspower is torque in time the higher RPM almost always overcompensates for falling torque for a little while.

As long as the torque falls at a rate slower than the rpms increase, then power will rise as torque falls.

P(hp) = [torque (ft-lbs) * rpm]/5252

The 5252 is the conversion factor from ft-lbs-rotation/minute to hp

I guess in conclusion there is no way to figure how many HP a pound is worth. However since getting them off the rider is more likely to reduce aerodynamic drag (read less girth through the air) that might be the most profitable in terms of top speed while getting them off the rotating mass makes the most sense for acceleration.

I don't follow your conclusion.

Here is how I did it. We will assume acceleration on a flat surface (no hills) to keep things simple. Here is the calculation. Sorry it does involve math, but math is the language of physics.





So if I add 1 hp to my bike, the amount of weight I need to add to have it accelerate at the same rate (same change in speed/ the same time) regardless of gear, would equal the original weight to power ratio. Therefore, the equivalent of 1 hp is your current weight to power ratio. Since you are not inceasing the power by losing weight, you will not gain any top speed, but your bike will increase acceleration.

[spyderchick]

Brian, I think we should put that on the back of your leathers.  ;D

[tzracer]

http://scienceworld.wolfram.com/physics/SchroedingerEquation.html

equation 1 would be more fun.

[HAWK]

Brian,

Let's take a specific bike, say that R6 you mentioned.

Let's actually take 2 of them to the drag strip. One with 13:49 sprocket set and one with a 17:49 sprocket set (again, being a twin rider I apologise if my selection of gearing is a little off). Which bike has more horsepower on the dyno? and which will arrive at the end of the drag strip first?

The bike with the shorter gear of 13:49 will arrive at the finish line first as it will have better acceleration due to the extra torque multiplication of the final drive and since I don't believe the R6 is capable of terminal velocity in a standing 1/4 mile the engine redline should not limit either bike.

Now were we to take this roadshow to Bonneville the outcome would be a little different. While the bike with 13:49 gears would accelerate faster, and since both bikes have the same horsepower the terminal velocity would be the same, the bike with 17:49 gears would have a much higher probability of still having an engine in operable condition after a 5 mile run (might also add that there is a possibility that the 13:49 bike would run out of its power band  before reaching its theoretical terminal velocity).

All of this would be moot except for the basis of this thread. Your calculations should be using the weight to torque ratio of the bike+rider. I am going to have to go online and find some specs for various bikes and run some numbers but I think a more constant/duplicatable/meaningful question might be how many pounds to gain one rear tooth.

[tzracer]

The basis of the discussion was no changes except for weight.

Using torque muddies the issue because there is not one figure for torque (dynos give crank torque). As you pointed out the torque value (at the rear wheel) changes based upon gearing. So what value to use?

The original point was to find the weight needed to be lost that would be equivalent to gaining 1 hp.

Changes in acceleration due to gearing are easy to calculate, it is just the percent change in the gearing.

Aside : In your example, the R6 with the shorter gearing may not win the drag race. It could top out in 6th gear before the end of the strip, it may be ddifficult to launch due to such short gearing, you will have to shift more.

[spyderchick]

http://scienceworld.wolfram.com/physics/SchroedingerEquation.html

equation 1 would be more fun.

Along with a cat.  ;)

[tzracer]

Along with a cat.  ;)

In a box.....maybe.....

[spyderchick]

In a box.....maybe.....

don't forget the gieger counter. =^..^=

[HAWK]

Uncle :P
I'm still having a problem with the whole acceleration vs torque vs horsepower thing.

What I have learned here is that horsepower is in fact related to acceleration although I still haven't quite got my head fully wrapped around the exact relationship.

The original point was to find the weight needed to be lost that would be equivalent to gaining 1 hp.

Changes in acceleration due to gearing are easy to calculate, it is just the percent change in the gearing.

In looking at your proof I noticed something, while the weight difference on the more powerful bike is smaller (lose less weight to make 1 HP) the value of that 1 HP is less (600lbs rider+bike with 100 HP will go 1% faster with 1 HP increase, 600lbs rider+bike with 200 HP will go .5% faster with 1 HP increase). I think there is a specific number of pounds for a HP gain of 1% that would apply to all bikes.

Paul