Effects of changing gear ratios

[UselessPickles]

This isn't quite relevant to the FJR, since we can't simply change sprockets to adjust the overall gear reductions, but it's an interesting subject anyway...

What are the effects of changing the overall gearing of a bike (or any vehicle, for that matter)? The common misconception is that taller gearing gives you higher top speed, but less acceleration, while shorter gearing gives you more acceleration, but a lower top speed. Those generalizations have partial truths to them, but people seem to misinterpret the idea to mean "shorter gearing means that I can accelerate faster across the board!"

Time for some visual aid:

Exact values are intentionally left off this chart to avoid focusing on unimportant details. Before anyone asks: NO! this is not Gen I gearing vs Gen II gearing. This is just two different arbitrarily different gear ratios for illustrating the trends in taller vs shorter gearing.

Explanation of the parts of this chart:

The two jagged mountain lines represent the amount of force applied by the rear wheel at full throttle when in the best possible gear for max acceleration at any given speed. One line represents tall gearing, and the other is short gearing. The gear shifts are pretty easy to spot - they're the creases in the lines.

The "Max Power" dashed line shows how much force the rear wheel would apply if max power was available at all speeds. This is essentially what a CVT (continuously variable transmission) could do.

The "Redline Power" dashed line shows how much force the rear wheel would apply if the engine was running at maximum RPMs at all speeds.

The "Drag Force" line shows how much rearward force is applied by aerodynamic drag at all speeds.

The "Max Force" dashed line represents the most most rear wheel force that can be practically applied to the road. This could be the point at which the bike starts to wheelie, or the back tire loses traction and starts making smoke. Either way, if you see the rear wheel force line go above this "Max Force", you would need to use less than 100% throttle at that point to keep the wheel force at/below the max.

Analysis of the chart:

Acceleration is directly proportional to rear wheel force minus the drag force. Top speed is determined by where the two lines intersect.

I hereby declare that the "Power Corridor" is the space between the "Max Power" line and the "Redline Power" line.

Ideally, once you reach peak power in 1st gear, the rear wheel force should never fall outside of this "Power Corridor". On the FJR, 1st and 2nd gear are too far apart from each other, so they don't actually intersect, and the RPMs fall back too far when shifting into 2nd to stay in the "Power Corridor".

No matter what you do to the overall gearing, the rear wheel force will always follow the "Power Corridor" (except for the beginning of 1st gear, which will always be outside of the corridor). Shorter gearing "squishes" the entire tire force line left and up within the corridor, and taller gearing "stretches" it right and down within the corridor.

Adding more gears to the transmission would allow you to "tighten up" the rear wheel force line so that it stays closer to the "Max Power" line, rather than bouncing back and forth so much.

Shorter gearing can improve acceleration in first gear to a certain point. Anything that goes above the "Max Force" line is useless and just makes the bike harder to ride.

Shorter gearing does NOT improve acceleration everywhere. After 1st gear, it just causes the peaks and valleys of the wheel force line to move around within the power corridor. In some areas you'll have more acceleration with shorter gearing, but in other areas you will have less acceleration.

Taller gearing will only give you more top speed if the original gearing had peak power in top gear occurring before top speed. Go too tall, and you'll start decreasing your top speed. Best possible top speed is achieved when the bike is geared to have peak power at the speed where "Drag Force" and "Max Power" intersect.

Gearing changes alone cannot give significant top speed increases, unless the bike was geared incredibly so low that it reaches max RPM before "running into" the drag force line. If a bike is already limited in top speed by drag, then the only way to significantly increase top speed is to reduce drag (improve aerodynamics) and/or increase power. The amount of power required to overcome drag is proportional to the cube of speed. This means that doubling the top speed would require 8 times the power!

To put the effects on top speed in perspective, the difference between the best possible and worst possible drag-limited top speeds on the FJR is only 3.5mph.

 

[lnewlf]

This is a great intellectual approach to the subject and in my limited experience spot on. Most quarter miles are won or lost in the hole shot. As with the FJR too tall gearing makes the launch harder-high rpm must be used and the clutch modulated just right to avoid bogging or wheelspin- and there is always the fear of turning into a human flyswatter. Once she's hooked up a close ratio tranny is needed to stay on top of the power curve and use all the gears thru the traps. Almost never does agood quarter mile anything make a good daily driver. My old 340 Duster which was a decent car to drive in stock trim and would run low 14's was a pain to drive by the time it would run high 11's.

 

[scubatech]

Excellent reading for those of us that have played around a lot with racing and performance in general. I have always enjoyed reading this stuff,numbers don't lie. thanks.

 

[Fred W]

I think that the piece that is missing in this analysis is time.

The bike with the shorter gearing will reach a given point in the speed vs force X-Y graph in a shorter period of elapsed time than the taller geared bike will. speed/time = acceleration

 

[Road_Runner]

I think that the piece that is missing in this analysis is time.

The bike with the shorter gearing will reach a given point in the speed vs force X-Y graph in a shorter period of elapsed time than the taller geared bike will. speed/time = acceleration

+1 on the above statement... the higher numbers at the start of the graph for the shorter geared bike would put it a good bit ahead off the line.

Change ratios on a higher redline bike that makes it peak power at 10-12K RPM and differences in 1/4 mile time become greater.

 

[UselessPickles]

I think that the piece that is missing in this analysis is time.

The bike with the shorter gearing will reach a given point in the speed vs force X-Y graph in a shorter period of elapsed time than the taller geared bike will. speed/time = acceleration

There's no generalizations that will work for determining which bike would win a race, because it all depends on how different the gearing is, what speed you start the race at, and how long the race is (race to a distance? speed? for a specified time?). Any specific race conditions would need to be calculated out by simulating the acceleration over time to produce speed/position results over time.

In this example, if you start at a low speed in 1st gear with the clutch fully engaged, then yes, the shorter gearing will initially accelerate faster and gain a speed/distance distance lead, and the taller gearing may or may not catch up, depending on the ending speed/distance.

If you start the race at a speed that is near the end of 1st gear , the taller gearing will get the initial lead.

If you do a standing start, then the taller gearing will have the earliest advantage. When launching from a start, you can slip the clutch to get the engine at any RPMs you want, which will allow you to choose any level of acceleration that is available in 1st gear for your launch. In this example, both bikes are capable of exceeding the max usable rear wheel force. That means both bikes are capable of launching just as fast as each other, up until the wheel force lines drop back down below the max force line. The bike with taller gearing will be easier to launch without exceeding the max usable force, and it will out-accelerate the shorter gearing at the end of 1st gear, gaining a speed/distance lead.

If the "max force" line was higher than the peak of the taller gearing's wheel force line, then the lower gearing would have an advantage through much of first gear when launching, and would likely gain a lead from the launch that the taller gearing could not catch up to.

 

[Fred W]

I understand what you are saying about the equalizing effect that wheel slip would have on the launch, but I think you are missing something (just not sure what) or else I am.

My simple mind says that (after exceeding the point of wheel slip) having the mechanical advantage of lower gearing allows the bike's engine to apply more torque to the rear wheel (and ground). This has to result in quicker acceleration rates through all of the gears.

All other things being equal, it shouldn't be until after the shorter geared bike exceeds maximum power in top gear that the taller one would "catch up".

 

[UselessPickles]

If you look at it based on engine speed only, then yes, shorter gearing will always have a mechanical advantage over taller gearing at any given RPM. But it's ground speed that matters. Shorter gearing gains mechanical advantage at any given RPM, but equally loses ground speed at that RPM. Throwing in gear shifts and the variation of torque over RPMs (the shape of the torque curve) further complicates things and makes it nearly impossible to conceptualize in your head how everything will balance out in the end.

This is why I made the chart. It shows how much actual force can be applied by the wheel at any given speed for two different overall gearing ratios, using the same torque curve. Pick any horizontal position on the chart. Whichever wheel force line is higher at that point indicates which can accelerate faster at that speed. If both bikes were cruising at a specific speed (in whatever gear is optimal for acceleration at that speed), then both whacked the throttle open, the bike with the the higher wheel force line at that speed will accelerate faster and gain a lead.

As you pointed out, this is a graph of force vs speed. It only indicates which bike accelerates faster at each speed, but not which bike would be further ahead in either speed or distance in a race at any given time. To get results based on time is more complicated because acceleration changes speed over time, and the amount of acceleration at any given time is dependent on the speed. As I described in my previous post, initial/terminating conditions can greatly affect the outcome (starting speed? clutch fully engaged? race to a distance? race to a speed? race for an amount of time?), so I can't provide just one chart that show's which bike would be ahead at any given time. I can, however, simulate races if I choose the initial and terminating conditions.

 

[carlson_mn]

Going from my VStream to a shorter than stock Cee Bailey's made for a 5mph increase in top speed on my bike. And I like the top end acceleration better on my Gen2 a bit better. My seat of the pants feeling is what I see in your graphs, nice.

 

[UselessPickles]

... I like the top end acceleration better on my Gen2 a bit better. My seat of the pants feeling is what I see in your graphs, nice.

Before anyone asks: NO! this is not Gen I gearing vs Gen II gearing. This is just two different arbitrarily different gear ratios for illustrating the trends in taller vs shorter gearing.

 

[madmike2]

Just after the Stone Age....which is about when I began to play around with engines, transmissions and gears.....once we determined that steam power wasn't the answer for us....I seem to remember that we'd determine what RPM the engine would turn and there was a formula for the gear ratio:tire diameter for the top end we expected to run.

There are so many variables: weight; horsepower; tire diameter; wind resistance; etc.

I do remember, at a national event, that one of my buddies had blown up the engine in his '57 Chevy gasser and they took the 3rd member out (5.38s, IIRC) and plugged in into another friends 6-cyl.x4 speed Chevy Nova (running M/stock, or something). That guy ended up winning at his first level because the car would launch hard and disappear while his competition was waiting for their "tree" to count down. Most of his opponents would re-light because the car left the start line so strong.

We, on the other hand, would stand about 1/2 track and listen to the little Nova go into valve float @ 1/8-3/16 mile as he held the throttle down. Great fun!

IIRC, the car wasn't any quicker at the finish line...and certainly didn't have the top end....but it sure played mind games with his competitors. Once he moved up into eliminations, other class winners were more used to running against themselves.....

adendum: Unbelievable! I went rooting through a drawer and found an old "Power-Speed Calculator" from HotRod Magazine that has to be from the late 60s or early 70s.

This IS a great academic exercise and a fun discussion to read.

 

[UselessPickles]

BTW - to put the effects on top speed in perspective, the difference between the best possible and worst possible drag-limited top speeds on the FJR is only 3.5mph.

(first post updated to contain this tidbit)