Effects of changing sprockets


UselessPickles

New Member
NOTE: The following and much of the resulting discussion in this thread relates to how gearing changes affect full throttle acceleration when shifting gears as appropriate such that you are getting the best possible acceleration out of the bike at any given speed (like drag racing). There is some useful discussion later in the thread about how gearing changes will effect "normal" daily-driving type riding here: http://www.600cc.org/forum/f89/effects-changing-sprockets-23986/index7.html#post413514

I originally posted this on a Yamaha FJR1300 forum. Since quite a few people seem to change sprockets on the FZ6R, I thought it would be useful to post this here too. There are a few references to the FJR, but it is mostly generic info. When you see "taller gearing", think "larger front sprocket" and/or "smaller rear sprocket". The opposite for "shorter gearing".

****** BEGIN COPY FROM FJR FORUM ******

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!

****** END COPY FROM FJR FORUM ******


Here's the original thread with some additional discussion: Effects of changing gear ratios - FJRForum
 
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UselessPickles

New Member
Wow... nothing? I hope I didn't fry all your brains :)


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.
 

UselessPickles

New Member
This is bound to get some more reactions...

I simulated a comparison between stock gearing, the common -1/+2 gearing that people use for "more acceleration", and the common +1/+0 gearing that people use for lower cruising RPMs (and accurate speedo readings), but sometimes fear loss of acceleration. Simulated with a 170lb rider, at SAE standard air conditions (77°F, 990mbar pressure, 0% humidity), shifting at optimal points for max acceleration, and 0.32s spent shifting (that's how fast my clutchless shifts are). 1/4 mile runs assume 11 inches of "roll-out" (amount of travel at the start line before the timer actually starts). Aerodynamic drag was based on a reported actual (not speedo-indicated) top speed of 125mph from some motorcycle website.

The "soft launch" is at 3000rpm, which is probably comparable to a casual quick launch (taking off from a light quickly, and going to full throttle right away, but not revving the crap out the engine to get a drag-racing launch).

The "hard launch" is at 8000rpm. This is the fastest possible launch, and also assumes that you launch perfectly so that you are using full throttle during the whole launch and working the clutch to keep the engine at 8000rpm.

(more sprocket combinations have been added than what I listed above)

Fastest results in each grouping are bold.
Slowest results in each grouping are red.

*NOTE*
I don't know at what point the FZ6R will begin to wheelie, so the times for the shorter gearings are possibly unrealistic. The point at which it will begin to wheelie depends much on how high/rearward is the center of mass of the the entire bike+rider system. That means that if you are a heavier rider and/or have a passenger and/or are sitting upright rather than laying on the tank, you are less likely to be able to actually make use of the extra early (1st gear) acceleration of the shorter gearings.

0-60mph (soft launch)
-1/+2: 3.94s
-1/+1: 4.00s
-1/+0: 4.06s
Stock: 4.26s
+1/+0: 4.46s

0-60mph (hard launch)
-1/+2: 3.54s
-1/+1: 3.58s
-1/+0: 3.62s
Stock: 3.75s
+1/+0: 3.89s

0-100mph (soft launch)
-1/+2: 11.47s
-1/+1: 10.94s
-1/+0: 11.04s
Stock: 11.39s
+1/+0: 11.06s

0-100mph (hard launch - 8000rpm)
-1/+2: 11.07s
-1/+1: 10.53s
-1/+0: 10.60s
Stock: 10.89s
+1/+0: 10.49s

1/4 mile (soft launch)
-1/+2: 12.56s @ 105.3mph
-1/+1: 12.57s @ 104.9mph
-1/+0: 12.59s @ 104.5mph
Stock: 12.66s @ 105.9mph
+1/+0: 12.75s @ 104.8mph

1/4 mile (hard launch)
-1/+2: 12.23s @ 105.4mph
-1/+1: 12.24s @ 105.1mph
-1/+0: 12.24s @ 104.6mph
Stock: 12.25s @ 106.1mph
+1/+0: 12.28s @ 105.0mph

Top Speed
-1/+2: 122.9mph
-1/+1: 123.3mph
-1/+0: 123.6mph
Stock: 125.0mph
+1/+0: 126.2mph


There you go. Lots of numbers to compare different sprocket sizes. This clearly shows that shorter gearing does not always mean more acceleration. The top speeds do actually somewhat follow "conventional wisdom" this time, in that the taller gearing gives higher top speeds, but not for the reasons that people usually think.
 
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djf18374

New Member
Is this for the FJR1300? What year?
This appears to be for the FZ6R, since there are sprocket changes mentioned, and the numbers are exactly those for the 6R. 126 MPH corrected seems about right for the +1 +0 gearing.
 
F

FZ6R_Blue

These numbers cant be right. i have had mine up to about 145 on a flat stretch of road

Top Speed
-1/+2: 122.9mph
Stock: 125.0mph
+1/+0: 126.2mph
 

UselessPickles

New Member
Is this for the FJR1300? What year?
The first post is just generic info. The sprocket size comparison is for the FZ6R. The FJR has a shaft drive, the overall gear ratio cannot be changed.

These numbers cant be right. i have had mine up to about 145 on a flat stretch of road
Indicated speedo speed, or actual GPS speed? Any wind? Do you know the road was level? A slight downhill slope and a tailwind can add a lot of top speed. If you have -1/+2 sprockets, then your speedo will be quite optimistic. Like I said in the post, the aerodynamic drag I used is based on a reported top speed of 125mph from a motorcycle website (can't remember which one). Without knowing you at all, I'd have to put my faith in the motorcycle website for having a better testing procedure to minimize error (probably multiple runs in opposite directions, average results, using GPS or radar gun).

Also, the exact numbers don't matter anyway. Just look at the relative comparison between the sprocket sizes.
 
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UselessPickles

New Member
These numbers cant be right. i have had mine up to about 145 on a flat stretch of road
So the most likely way you got to 145mph was by using -1/+2 gearing and looking at your speedometer.

Redline is at 11500rpm. You can't go faster than that. With stock gearing, that would be 138mph (but you can't get there due to drag). With -1/+2 gearing, you would be at 124mph (actual speed). An actual speed of 145mph is just impossible.

A stock bike has already been shown to have about 6% speedo error (+1/+0 sprockets are 6.25% taller than stock and seem to make the speedo accurate).

Stock gearing is 11.3% taller than -1/+2.

That gives a grand total of 18.3% speedo error with -1/+2 gearing, so your 145mph speedo reading would be an actual speed of 145mph / 1.183 = 122.6mph, which is very close to my simulated top speed of 122.9mph.
 

djf18374

New Member
So the most likely way you got to 145mph was by using -1/+2 gearing and looking at your speedometer.

Redline is at 11500rpm. You can't go faster than that. With stock gearing, that would be 138mph (but you can't get there due to drag). With -1/+2 gearing, you would be at 124mph (actual speed). An actual speed of 145mph is just impossible.

A stock bike has already been shown to have about 6% speedo error (+1/+0 sprockets are 6.25% taller than stock and seem to make the speedo accurate).

Stock gearing is 11.3% taller than -1/+2.

That gives a grand total of 18.3% speedo error with -1/+2 gearing, so your 145mph speedo reading would be an actual speed of 145mph / 1.183 = 122.6mph, which is very close to my simulated top speed of 122.9mph.
Thank you. I was going to go through the math and explain this exact thing to Mr. Blue...but you did all the work for me :) I find a lot of people trusting their speedo to be accurate from the factory. Even worse, they think the speedometer should still be accurate after changing the sprockets to a different ratio :eek:
It's math, plain and simple math, and the physics of drag have not changed. our HP of the FZ6R just can't overcome the drag force at those speeds. ~125 MPH actual speed is all she wrote, on flat road.
Downhill may be a different story... :zombie:
 

dart1963

Super Moderator
Elite Member

MNGreg

waiting out winter
Elite Member

djf18374

New Member
So to get an accurate speedometer, I want to go for +1 front and stock rear? So if this lowers the cruising rpm, shouldn't that also help improve your gas mpg also?

Sent from my SCH-I500 using Tapatalk
Yes, brings the speedo to within 0.5 MPH of GPS speed output to go up 1 tooth on the front. It also therefore corrects your odometer output, so you may measure the same MPG (using the odometer as before), but it is actually higher than before the swap.
Example from my personal experience:
a. Stock gearing - measured MPG = 45 MPG (actual MPG = 42 with `6% correction factor)
b. +1 up front - measured MPG = 44MPG, which is now true MPG since the odometer is reading actual miles traveled.

:thumbup:
 

UselessPickles

New Member
Can you do -1,+0 .
I updated my comparison post with -1/+0 sprockets.

I also highlighted best and worst numbers in each category and added this important note:

*NOTE*
I don't know at what point the FZ6R will begin to wheelie, so the times for the shorter gearings are possibly unrealistic. The point at which it will begin to wheelie depends much on how high/rearward is the center of mass of the the entire bike+rider system. That means that if you are a heavier rider and/or have a passenger and/or are sitting upright rather than laying on the tank, you are less likely to be able to actually make use of the extra early (1st gear) acceleration of the shorter gearings.


I do have the ability to limit acceleration to some max threshold in my simulation, so I could theoretically experimentally determine what amount of wheel force begins a wheelie for a specific weight of rider in a specific riding position and recalculate my results. But that would probably be difficult to do, and in the end, the results would only apply to that specific rider. So the disclaimer above is the best you'll get :)
 

UselessPickles

New Member
** EDIT: NOW FIXED! **

Crap... I just noticed I had left a temporary change in my code that could make the results inaccurate (I had increased the time step to 0.01s to make it easier to debug a problem at one point, and never returned it to a more accurate time step of 0.001s).

I'll be working on updating all the numbers. I'll post when they're all updated.
 
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Millhouse

New Member
This thread really helped me out as I was thinking about changing my gearing to -1 +0. So all these times you show are assuming stock horsepower? Would there be any way to change the equation to show the times with a modded bike? Add 7-8hp for a pipe and power commander?
 

UselessPickles

New Member
It's not just based on stock horsepower, but on the entire stock torque curve. At any moment of time in my simulation, I know how fast the bike is currently going and what gear it's in. From that, I look back to the torque curve at the RPMs that would get that speed in that gear to find out how much torque to simulate. Torque is multiplied by overall reduction ratio for that gear and divided by wheel radius to get wheel force. Force due to drag at that speed is subtracted, and the resulting net force is divided my mass of the bike+rider to determine acceleration for the next 1/1000 of a second of the simulation. Position of the bike is updated based on the current speed, and speed is updated based on the calculated acceleration. Rinse and repeat about 12,250 times until the total distance covered is 1/4 mile, and I now know the time it takes for the stock bike to do a 1/4 mile and how fast it will be going at the end.

Since I need the whole torque curve for the simulation, and exhaust and tuning don't simply "add horsepower" or add some percentage of torque across all RPMs, there's nothing I could do about simulating a modded bike unless I had the torque curve from that modded bike.
 

traverser

New Member
A plus and minus for going +1 in the front.

The plus was I got longer chain life out of a previous bike I did this to. The theory is that the links don't have to bend as much, therefor the chain last longer.

The minus was on the previous two chains I ran. I did notice I had a bit more chain stretch than the prior chain when all was done, but that could have been many factors, engine braking, driving up mountains a couple of times, instead of my sealevel no hills or frills home that the last chain didn't see.

I used the same manufacturer chain type, replaced chain 1 @ 7k miles, chain 2 and 3 both changed at 9 -9.5K miles. Chain 2 had stretch an extra 8 MM over chain 1, and Chain 3 was 9 mm over chain 1. I had a 520 conversion on a stock geared sv650 for chain 1, and a +1 front on chain 2 and 3.

Note I didn't race the engine much. 9 MM seems like a lot, but not when you count the number of links in that chain; (108 link chain, or 0.083333 per link be specific.)
 


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