Usefull Information on Gearing and Sprockets for those who are interested. Part One.

Hey all, I just thought I'd put together a thread on aftermarket gearing and final drive ratios as well as the math involved with figuring them. There have been several questions and threads on this over the past couple of weeks and I am going to try and condense all the information down into one usefull guide that should be able to be used by anyone wanting to run aftermarket gears. One of the most inexpensive but most powerful mods any gsxr owner can do to their investment is run an aftermarket final drive ratio. What does this mean? It means that you change the gear ratio between the front and rear sprockets by purchasing aftermarket sprockets with a different number of teeth than factory. Usually those that do this reduce the ratio (creating a gear reduction) so as to aid in acceleration and torque. Some major benefits to doing this include reducing wear on clutch plates, increasing torque throughout the tach, and increasing acceleration rates. This makes it a mod that can be enjoyed by stunters, riders, and drag enthusiasts alike. However in the world of physics a trade must be made in order to achieve greater acceleration. You have to reduce speed. Therefore the more power, the less speed. There are a few things to take into consideration when thinking about aftermarket gearing. Most inportantly is what are you going to use the bike for. Other factors include, gas mileage, top end speed, driving conditions, etc... Here are a few mathematical principles to take into consideration before we begin..... 1.) We will be using three variables during the calculations. These variables are RPM, your compound gear ratio, and tire size. If you have any two of these variables the third one can be found. For example.... if 2+3=x then x-2=3 and x-3=2. 2.) If you have a decimal such as .876 it is equal to 87.6%. Just move the decimal two places to the right and add a percent sign to change a decimal into a percent and vica versa to change a percent into a decimal. 3.) When figuring a gear ratio divide the number of teeth on each gear that power is being transferred to in the opposite order that power is travelling. For example.... If power is transferred FROM the transmission mainshaft gear with 39 teeth TO the transmission countershaft with a gear that has 77 teeth, then we would divide 77 by 39 to get 1.974. This means that everytime the transmission mainshaft turns 1.974 revolutions the transmission countershaft turns 1 revolution. This can be written as 1.974:1. 4.) When trying to figure your "aftermarket" speed based upon gear ratios, always divide the smaller number by the bigger number if you have decreased your ratio and always divide the bigger number by the smaller number if you have increased your ratio. For example.... If your stock final drive ratio is 2.687:1 and you LOWERED your gear ratio to 3.066:1 then you would divide 2.687 by 3.066 to get 0.876. This decimal figure represents how fast or slow your factory gear ratio is compared to your aftermarket gear ratio. It means that your factory gear ratio is 87.6% of you aftermarket gear ratio. Which also means that your only traveling 87.6% of your aftermarket indicated speed. Ok, on to the basics........... Here's a few questions and answers then we'll move on to the harder stuff........... I brought a bike with +3 in rear and -1 in front so my speedometer is off and as per advice on this forum i have decided to install speedohealer but in the meanwhile i need to know how does this configuration affect speed displayed in speedometer lets say i am doing 60mph as per speedo am i going faster than the speedo indicates or slower. thanks With +3/-1 you are going to see faster on the speedo than you are really going....... i went +3/-1 on my k6 600 and i am actually going 87% as fast as my speedo registers at any given time. This is how you can figure it. 1.) find out what the stock # of teeth are for your front and rear sprockets. 2.) divide the rear sprocket teeth by the front sprocket teeth and this will give you your stock final drive ratio. 3.) do the same thing as step two only with the aftermarket sprockets and this will give you your aftermarket final drive ratio. 4.) after you have the stock final drive ratio divide that by the aftermarket final drive ratio and this will give you a decimal number such as .8704532...... and so on (this is an example for mine.) Now all I do is take what speed is registering on my speedo and multiply that by the decimal number I got. Example...... factory final drive for my bike = 16T front and 43T rear 43/16= 2.687 aftermarket final drive for my bike = 15T front and 46T rear 46/15 = 3.066666666 Now I take factory FD / aftermarket FD whick is 2.687/3.066= 0.8763 All in all this means that my factory final drive ratio is 87.6% (.8763) of what my aftermarket final drive ratio is. And if the bike speedo still thinks my final drive ratio is factory then at any given time i am only going 87.6% of what the speedo says. Here's a simple explanation of why the speedo thinks i am going faster than i really am. The speedo is constantly doing math (the same math that we will be using later). However the only thing the speedo can change during its mathematical operations is the RPM variable. It uses the factory inputted gearing and tire size. If you change either one of these and the computer doesnt realize it then the calculations will be off. In this case the speedo thinks we are travelling at 8000RPM with factory gearing. However we have lowered the gear ratio and the bikes still thinks we are going 94 at 8000RPM when at 8000RPM we are only going 87.2% that fast. I hope that wasnt too redundent and it helps you...... Sooo, if his speedo says 100 then it's really 87.6. Simple. Exactly of course that would be if you started with the same setup as mine and you ended up with the same aftermarket setup as mine..... You may have to take the formulas and substitute in your own factory and aftermarket gearing...... I could be wrong but if your bike isnt a 600 or is a different year than mine then you may have different factory gearing and will have to vary my equation a little......... I'll write up some algebra for it later......then you can just plug and play the variables.... so basically if Stock gearing is 42/17t and i go down 2 in the front to a 15t/42 speedo says 186 but actually its only doing around 160mph ?:headscrat Basically the more rpm you turn..... the more off the speedo is..... my speedo is off about 3 mph per 2000 rpm..... so if im going 16000 rpm then speedo is gonna be about 24 mph off......... pretty simple math really..... and as for the above you dont have to crunch numbers on the fly to figure your speed without a speedo healer..... use the basic 10 method and just remember how many percent off it is....... if my speedo says 80 and you are at 87.6 percent like mine then i just think to myself 10 percent of 80 is 8 then i mulptiply that by about 9 (if 10% is 8.76 then 87.6% will be about 9 times that amount) and add a few to be close...... that will be close enough to ward off most speeding tickets...... unless your cops havent had their doughnuts for the day...... then it wont matter ..... 42/17= 2.470 (stock final drive) 42/15= 2.800 (aftermarket final drive) 2.470/2.8= .8820 (percent of SFD as compared to AFD) So, at any given time, 88.2% of what your speedo says is the actual speed you are doing...... For 186 mph this would be........ 186*.882= 164.05mph At ....... you are acutally going....... 20mph = 17.64mph 30mph = 26.46mph 40mph = 35.38mph 50mph = 44.1mph 60mph = 52.92mph 70 mph = 61.74mph 80mph = 70.56mph 90mph = 79.38mph 100mph = 88.2mph Theoretical number dont work. Do they take into account weight and air resistance? My 01 750 with FI mapping and a -1 maxes at 155 redline. I doubt a 15 tooth front can do 165. A lot of people think that they are trying to figure out what the top speed of their bike is...... That is definately not what we're trying to do here. We are taking facts and putting them into an equation to figure the answer which is basically the same thing your speedo does. If we WERE trying to figure the potential energy of our bikes then yes we would need to tak into account wind resistance, rider weight, and many many other physical things.. There's nothing thoretical about math...... if his speedo says 186 with that gearing then he is going about 165 plain and simple....... if air and weight were an issue then his speedo wouldnt say 186, his ENGINE wouldnt have enough power to get him there and he would only be doing 88.2% of whatever his speedo says....... OK, here is the most drawn out, boring, and physically demanding way to figure speed with the same type of mathematical algorithms your speedo and ecu use...... this will also help anyone who is interested in figuring what gearing to use before actually making the purchase and testing it out on your own...... You will be able to figure what the bike can and will do (so far as speed and RPM go) before you ever install them.

Speed is figured by a simple math formula used by your speedometer. It uses factory inputs on gear ratios and tire size, plus the RPM variable to figure speed. Any change in these three items and the speed will change. A speedo healer corrects this issue by changing one or more of those three variables to recalculate speed at any given rpm. (as rpm changes so does speed) the speedo is constantly doing math and has a small microprocessor that computes a mathematical algorithm based upon the rpm variable since the factory speedo thinks that the gearing and tires will always stay the same. When you change those the speedo still figures the speed based upon the factory gearing becasue it cannot take into account a change in gearing, therefore the speedo outputs the "wrong answer" (your speed) because it does not have the right information. Speed is based upon MATH and MATH alone. The last time I checked i never had to input my weight, driving conditions, my bikes weight, air drift , air drag, or any other physical attributes associated with riding to figure my speed. It is plain and simple that if you have this gearing with this tire and you are turning this rpm you are giong to be traveling this fast....... Simple as that....... The only three limiting factors to this equation are engine rpm redline, engine power, and factory electronic governors. If the engine cant turn the rpm then it wont go that fast. If the engine does not have enough power to carry the bike and rider to a certain rpm then it wont go that fast. (Usually not a problem with anything bigger than a 600. ) And if the factory doesnt want you to go over a certain speed based on math by rpm then they can limit that electronically. This is the formula........ First lets go over the different variables and give some simple explanations.... Primary Reduction Ratio - The gear ratio between the crankshaft and transmission mainshaft. In my bike (k6 600) the crank has a drive gear with 39 teeth which meshes with a gear on my mainshaft that has 77 teeth. You always divide the gear teeth in the opposite order that power passes through them. For example, the crank transmits power to the transmission mainshaft so we will say that 77T divided by 39T equals our ratio which is 1.974:1. This means that every time the crank makes 1.974 revolutions the tranny mainshaft makes 1 revolution thus giving us a "gear reduction" in rpm. Transmission Gear Ratio - This is the second step in transferring power to the tire. The power is emitted from the crank to the mainshaft and from the mainshaft to the coutershaft. The transmission mainshaft and coutershaft are in constant mesh which means the every gear (1st thu 6th) has one gear on the mainshaft and one gear on the countershaft that are always meshed together or are touching. The gears are selected by moving a synchronizer and activating a certain set of gears to each shaft. (it is much more complicated than that but im not here to explain the tranny right now) On my bike the ratios are as follows...... 1st = 2.785 or 39T on the countershaft and 14T on the mainshaft 2nd = 2.052 or 39/19 3rd = 1.714 pr 36/21 4th = 1.500 or 36/24 5th = 1.347 or 31/23 6th = 1.208 or 29/24 The whole numbers above for each gear in the tranny are obtained by dividing the gear teeth on the coutershaft with the gear teeth on the mainshaft. Basically just as in the primary reduction ratio this means that in 3rd gear everytime the mainshaft turns 1.714 times the couteshaft will make one full revolution. Again gving us even more "gear reduction". Final Reduction ratio - The third and final step in the power transfer process. This is also known earlier in this thread as the final drive ratio. This ratio is the most commonly known as it is the ratio between the front and rear sprockets. The coutershaft of the tranny sticks out of the case and is splined. This is where you will find your front sprocket held on with a nut. The front sprocket is connected to the rear sprocket via a chain which respresents the same thing as being in constant mesh with one another. This step transmits power from the transmission to the rear wheel. On my bike the front stock sprocket is 16T and the rear is 43T which makes a final redution ratio of 2.687:1. This means that when the front sprocket turns 2.687 times, the rear one will have made on revolution. Since the rear sprocket is driectly connected with the rear wheel via cush drive then we can deduct that everytime the rear sprocket makes on revolution so does the rear wheel assembly. Again giving us even more "gear reduction". We can assume with math then by mutiplying each one of these three gear ratios together we will get the total reduction ratio or compound ratio from the crank to the rear wheel. This number will be the primary ratio (times) the tranny gear ratio (times) the final drive ratio. It does not matter what tranmission gear ratio you choose at this point. In my case it is 1.974 * 2.052 (2nd) * 2.687 = 10.884. This number means that every time the crank turns 10.884 revolutions the rear wheel will make one revolution. Tire size - we will use tire size to determine how far the bike moves for every full rotation of the rear wheel assembly. Circumferece is the total distance around the outside of the tire. To figure circumference we need to mupltiply the tire diameter by pi (3.14) ....... To find tire diameter...... In my case I am running a 190/50 ZR17. The Z in this equation only represents the speed rating for the tire. The R represents wheel diameter. The 190 represents the width of the tire in mm. The 50 represents the aspect ratio. The aspect ratio means that the distance from the edge of the wheel to the top of the tire is "x" amount of the total width. In this case it will be 50% of 190mm or 95mm. We will start at the top of the tire and work our way across. SO, from the top of the tire to the wheel is 95mm. Then from the top of the wheel to the bottom of the wheel is 17 inches. And form the bottom of the wheel to the bottom of the tire is another 95mm. Now to get those pesky mm turned into inches..... There are 24.5 mm in one inch. So if we divide the mm by 24.5 it will give us inches. So 95mm x 2 = 190 mm / 24.5 = 7.755. This number plus the diamter of the wheel gives us the total diameter. So, 7.755 + 17 = 24.755 x 3.14 = 77.73 inches. (tire circumference) So now we know that everytime the rear whel makes one revolution it moves the bike 77.73 inches. Now it gets kinda complicated..... This is what we know so far...... The total reduction is 10.884:1..... The bike moves 77.73 inches everytime the rear tire makes one complete revolution. Now lets pick an rpm...... We'll say you are cruising down the interstate at 8000rpm. OK, everytime the crank turns 8000 revolutions the rear wheel is going to turn 8000/10.884 revolutions because when the crank turns once the rear wheel doesnt make a full revolution due to gearing. It only turns 1/10.884th of a revolution. SO when the crank turns 8000 times the rear wheel will turn 735.02 times. This all happened in ONE MINUTE (revolutions per MINUTE) So in one mintue the rear wheel turned 735.02 times. If every time the rear wheel makes one revolution it moves the bike 77.73 inches then we can say in 735.02 revolutions it moved the bike 735.02 * 77.73 = 57133.104 inches. Again this all happened in one minute. Now we can use info we all ready know cause we're all so smart.... such as.... there are 5280 feet in one mile..... and there are 60 minutes in one hour....... If the bike moved 57133.104 inches in one minute the it is safe to say that the bike moved 3427986.276 inches in one hour (57133.104 * 60). And it will also be safe to say that we can divide that by 12 and turn it into feet. This will be handy because the number is smaller and we know how many feet are in one mile.So, 3427986.276/12 = 285665.523. This number is how many feet the bike moved in one hour with a tire size of 190/50ZR17, a gear reduction of 10.884, and an rpm of 8000. If we divide that number by 5280 (number of feet in a mile) then we will get MPH. Which is 285665.523/5280 = 54.103 mph There you have it...... THis is the most complicated drawn out way you can possibly do this figure, but it is the most easy to understand after you think about it....... I hope everyone is thoroughly confused....... It is simple even though it may look intimidating..... It is nice to be abe to rely on math and not the electronic that others have made sometimes in my opinion...... I am oing to spend some time here in a minute to condense all this down into one simple algebra formual so you can just plug and play..... At 8000 rpm on my bike in second the speedo reads 54mph..... Id say that was pretty close...... If anyone has any more information or notices any errors in this thread please feel free to PM me or correct it on here..... I hope this was usefull for everyone If anything need explainedin more detail just let me know...... THANKS!!!!!

that is a good description. here is a link i found that is also very helpfull and you dont have to do all the math..lol plus it can help tell you the chain lenth you will need. http://www.xs4all.nl/~ator0437/gc/ just type in your bike description and it will walk you thru the rest.. most of our bikes are already in there..

that is a good description. here is a link i found that is also very helpfull and you dont have to do all the math..lol plus it can help tell you the chain lenth you will need. http://www.xs4all.nl/~ator0437/gc/ just type in your bike description and it will walk you thru the rest.. most of our bikes are already in there.. Thats an awesome program.......

MY BIKE HAS 3000 MILES ON HER IF I CHANGED THE SPROCKETS SHOULD I CHANGE THE CHAIN ALSO WITH SO LITTLE MILES ON IT THANKS B SAFE ON 1 OR 2 WHEELS:hmmm:

MY BIKE HAS 3000 MILES ON HER IF I CHANGED THE SPROCKETS SHOULD I CHANGE THE CHAIN ALSO WITH SO LITTLE MILES ON IT THANKS B SAFE ON 1 OR 2 WHEELS:hmmm: I did not change the chain on my k6 600 when i put on -1/+3 but i did however check the chain and factory sprockets over really well for wear before i made the decision to keep my factory chain..... my bike had about 3500 miles in it when i did this...... It has been recommended by others to change everything out when you change either the sprockets or the chain....... i think its a decision you have to make....

http://www.members.aol.com/rotaxjohn/Interactive.html http://www.dropbears.com/u/utilities/gearing.htm

..

someone should sticky this

lots of reading... ill do it later... or convert it into a mp3... that would be sweet:clap:

I did not change the chain on my k6 600 when i put on -1/+3 but i did however check the chain and factory sprockets over really well for wear before i made the decision to keep my factory chain..... my bike had about 3500 miles in it when i did this...... It has been recommended by others to change everything out when you change either the sprockets or the chain....... i think its a decision you have to make.... so if i go -1/+3 am i gaining accel. and losing top end? and are there any ways to add accel and not lose top end or too much top end?

how much top end am i losing with the 520 conversion? it is sad to say but i do some racing for money should i keep my 525 set up or should i go down to get a better jump off the line? by the way i have a 04' 750 drropped about 2"

so if i go -1/+3 am i gaining accel. and losing top end? and are there any ways to add accel and not lose top end or too much top end? To start, I would just drop -1 in front and see how you like it. Then if you still want more take-off power, start adding teeth in the back. +1 or +2 first. My -1/+2 is PLENTY for me and my 600. Might even put the rear back to stock. how much top end am i losing with the 520 conversion? it is sad to say but i do some racing for money should i keep my 525 set up or should i go down to get a better jump off the line? by the way i have a 04' 750 drropped about 2" 520/525 is just chain size. 525 is a lil stronger and will probably last a little longer but a little heavier.

To start, I would just drop -1 in front and see how you like it. Then if you still want more take-off power, start adding teeth in the back. +1 or +2 first. My -1/+2 is PLENTY for me and my 600. Might even put the rear back to stock. 520/525 is just chain size. 525 is a lil stronger and will probably last a little longer but a little heavier. yeah i had that conversion of a 520 on my 600 and it was an 01 and that thing came off the ground in first gear easy. had fun pulling wheelies on that thing but this 750 has more power and the tire jus seems to spin when i try to power it up in first gear. but i am going to try the 520 conversion kit on my 750 and see what it gives me

any one know the best 520 conversion kit or what maker and where would the cheapest place online to find one.

great info