Read This! RPM, Gear, Sprockets, Tire = Actual Speed!

[FinalImpact]

All,
After seeing all the threads about correcting the speedo error, top speed, tires, and how fast will an FZ go, I had to look a bit deeper. With that here is a formula that should give you the corrected speed based upon gear selection, sprocket choice, and tire diameter.

Obviously tire pressure and speed will change the rear tires rolling distance but I'm not going to get into that! In short if you have Stock Gearing and the manufactures recommended rear tire; If you hold your RPM's at 6,000 you should get the Speeds listed in Bold in all Six Gears (27, 40, 50, 59, 66 and 72mph)! There are other variables, but this should be pretty close. If you change sprockets or Tire diameter, use the formula to punch in the correct values so you can see how far off your speed is.

Formula is:

RPM * PIE * Tire Diameter (inches)
---------------------------------- = Speed in MPH
1056 (constant) * Actual Drive Ratio


So now we add in all the variables:

TIRE:
Stock Tire: 180, 55 ZR17 73W
Hint: Z rating is rated at 149mph with a max speed of (W) = 168mph
Tire Diameter: 24.8"
Circumference: 77.9"
Revs Per Mile: 813.39

Adding ACTUAL TIRE ROLL OUT DATA.....
Used mounted 37PSI:
Roll out: 75.5", wear passed tread bars
Tire OD: 24.03"

NEW mounted 37PSI:
Roll out: 77.375"
Tire OD: 24.63"
Tread bar depth near center: 0.22"

From: Old to New Tire Roll out vs Speedo Error = 2.5%

- - - - - - - - - - - - - - - - - - -

RATIOS:
Primary Ratio: Engine to Trans (PR): 86/44 = 1.9555
Secondary Ratio: Sprockets (SR): 46/16 = 2.8751
- - - - - - - - - - - - - - - - - - -

TRANSMISSION RATIOS:
G1 = 37/13 = 2.846
G2 = 37/19 = 1.947
G3 = 28/18 = 1.556
G4 = 32/24 = 1.333
G5 = 25/21 = 1.190
G6 = 26/24 = 1.083

- - - - - - - - - - - - - - - - - - -
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@

RPM * PIE * Tire Diameter (inches)
---------------------------------- = Speed in MPH
1056 * PR * SR * G#

@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@

1st Gear @ 6000 RPM:
6000 * 3.1415 * 24.8
---------------------------------- = 27.6MPH
1056 * 1.9555 * 2.8751 * (G1) 2.846


2nd Gear @ 6000 RPM:
6000 * 3.1415 * 24.8
---------------------------------- = 40.4MPH
1056 * 1.9555 * 2.8751 * (G2) 1.947


3rd Gear @ 6000 RPM:
6000 * 3.1415 * 24.8
---------------------------------- = 50.6MPH
1056 * 1.9555 * 2.8751 * (G3) 1.556


4th Gear @ 6000 RPM:
6000 * 3.1415 * 24.8
---------------------------------- = 59.0MPH
1056 * 1.9555 * 2.8751 * (G4) 1.333


5th Gear @ 6000 RPM:
6000 * 3.1415 * 24.8
---------------------------------- = 66.2MPH
1056 * 1.9555 * 2.8751 * (G5) 1.190


6th Gear @ 6000 RPM:
6000 * 3.1415 * 24.8
---------------------------------- = 72.7MPH
1056 * 1.9555 * 2.8751 * (G6) 1.083


haha! Confirmed! :thumbup: Speedo was correct!

2nd Gear @ 14,000 RPM:
14,000 * 3.1415 * 24.8
---------------------------------- = 94.3MPH
1056 * 1.9555 * 2.8751 * (G2) 1.947


Plug in the numbers for the variables on your bike and watch the tach! This should tell you pretty close to what your actual speed is!


To get the tires diameter use this!
Remember there are many variables so this is to get us "close"!

********************************************
Using a stock Tire Size of: 180/55 R17
The first number is the Tire's indicated section width in millimeters, measured from sidewall to sidewall. {180}/55R17

Section Width: 180 is converted to inches!
180mm / 25.4 = 7.0866"

Profile or Aspect Ratio: 55
The second number 180/{55}R17 is the tire's aspect ratio or profile.
55% or add a decimal point 0.55

Sidewall Height (SH):
SH = 7.0866" X 0.55 = 3.897"

Wheel Diameter (WD): 180/55R{17"}
WD = 17"

Tire Diameter in Inches:
SH + SH + WD = Tire Diameter
3.897" + 3.897" + 17" = 24.8"

********************************************


********************************************
I Hope you find this useful! If anyone sees any errors, let me know and I'll correct them!


Regards,
FI

JJD952 - Speed
EDIT: 2015-05-22, added real data from new and used tire

 

[Taku]

Einstein is that you?

 

[DownrangeFuture]

Nah, it's just basic algebraic proofs (haha, like proofs are easy) and tons of research.

Awesome work though. I got a half chub looking at all the maths.

 

[FinalImpact]

Thanks -

The fact is this; I redlined it in 2nd, I had to see of the speedo spoke the truth!

The basic math says yes it does! That's Crazy!!! Who knew 2nd would take us there! haha! :rockon:

 

[Evitzee]

That's good work. It would be interesting to see what the actual circumference of a new properly inflated tire is which will easily give the actual diameter so you could compare the calculated diameter to the actual.

 

[novaks47]

Great work!

You can input those gearing numbers, tire spec, primary ratio, and sprockets into this calculator, and see what difference sprockets will make. TW200 Speed Calculator

 

[FinalImpact]

That's good work. It would be interesting to see what the actual circumference of a new properly inflated tire is which will easily give the actual diameter so you could compare the calculated diameter to the actual.

You can do this easily!
Roll the bike to point where the valve stem is dead center at the bottom leaving enough room in front of you to roll it ahead one full rear tire revolution.

With the Valve stem dead center, mark a line on the floor aligning the stem. Roll the bike ahead one rear tire revolution and measure the distance! A stock tire should roll out 77.9". Repeat at least 3 times.

If its different, use the New Corrected number and divide that by PIE and enter it in the formula!

Lets say your tire measures 77.45". Just divide it by PIE!
77.45" / 3.141593 = 24.653"

What we don't know is how much does the tire grow at speed? It does grow some, but I don't know how much!

 

[YamaSpeed]

I know the speedo is accurate because I was going 135 Kph when I got a speeding ticket for being clocked at 135 Kph. :spank:

I also had these results confirmed by a second speeding ticket a week later.

That was three years ago now.

 

[FIZZER6]

Nice research and calculations!

I have used my GPS which is more accurate than any speedometer on any car I've used and the GPS shows my speedo to read ~7% high from 50-80 mph. Which is the way I like it....less likely to speed without knowing it!

 

[FinalImpact]

Great work!

You can input those gearing numbers, tire spec, primary ratio, and sprockets into this calculator, and see what difference sprockets will make. TW200 Speed Calculator

FWIW; it gives the same numbers I spewed out. Not that I'm advocating this, but you can do "Save As" and save the name.htm file to you're local drive and it seems to run as a stand alone.

This just lets you see how its done!

 

[FinalImpact]

You can do this easily!
Roll the bike to point where the valve stem is dead center at the bottom leaving enough room in front of you to roll it ahead one full rear tire revolution.

With the Valve stem dead center, mark a line on the floor aligning the stem. Roll the bike ahead one rear tire revolution and measure the distance! A stock tire should roll out 77.9". Repeat at least 3 times.

If its different, use the New Corrected number and divide that by PIE and enter it in the formula!

Lets say your tire measures 77.45". Just divide it by PIE!
77.45" / 3.141593 = 24.653"

What we don't know is how much does the tire grow at speed? It does grow some, but I don't know how much!

More thought on this: If its accurate under the posted speed limits that's all that really matters unless you're touting how fast your bike goes. . . Cause everything else is illegal! hahaha!

 

[deeptekkie]

I know the speedo is accurate because I was going 135 Kph when I got a speeding ticket for being clocked at 135 Kph. :spank:

I also had these results confirmed by a second speeding ticket a week later.

That was three years ago now.

Ditto! I was running 2-4 mph over the limit one day on the interstate and state trooper wheeled up behind me and latched onto me. I slowed to 73 mph, (which was only 2 over), and he seemed much happier.
He then proceeded to follow me for about three miles whilest close enough to easily read my tag with one eye tied behind him!

 

[deeptekkie]

All,
After seeing all the threads about correcting the speedo error, top speed, tires, and how fast will an FZ go, I had to look a bit deeper. With that here is a formula that should give you the corrected speed based upon gear selection, sprocket choice, and tire diameter.

Obviously tire pressure and speed will change the rear tires rolling distance but I'm not going to get into that! In short if you have Stock Gearing and the manufactures recommended rear tire; If you hold your RPM's at 6,000 you should get the Speeds listed in Bold in all Six Gears (27, 40, 50, 59, 66 and 72mph)! There are other variables, but this should be pretty close. If you change sprockets or Tire diameter, use the formula to punch in the correct values so you can see how far off your speed is.

Formula is:

RPM * PIE * Tire Diameter (inches)
---------------------------------- = Speed in MPH
1056 (constant) * Actual Drive Ratio


So now we add in all the variables:

TIRE:
Stock Tire: 180, 55 ZR17 73W
Hint: Z rating is rated at 149mph with a max speed of (W) = 168mph
Tire Diameter: 24.8"
Circumference: 77.9"
Revs Per Mile: 813.39
- - - - - - - - - - - - - - - - - - -

RATIOS:
Primary Ratio: Engine to Trans (PR): 86/44 = 1.9555
Secondary Ratio: Sprockets (SR): 46/16 = 2.8751
- - - - - - - - - - - - - - - - - - -

TRANSMISSION RATIOS:
G1 = 37/13 = 2.846
G2 = 37/19 = 1.947
G3 = 28/18 = 1.556
G4 = 32/24 = 1.333
G5 = 25/21 = 1.190
G6 = 26/24 = 1.083

- - - - - - - - - - - - - - - - - - -
@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@

RPM * PIE * Tire Diameter (inches)
---------------------------------- = Speed in MPH
1056 * PR * SR * GX

@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@

1st Gear @ 6000 RPM:
6000 * 3.1415 * 24.8
---------------------------------- = 27.6MPH
1056 * 1.9555 * 2.8751 * (G1) 2.846


2nd Gear @ 6000 RPM:
6000 * 3.1415 * 24.8
---------------------------------- = 40.4MPH
1056 * 1.9555 * 2.8751 * (G2) 1.947


3rd Gear @ 6000 RPM:
6000 * 3.1415 * 24.8
---------------------------------- = 50.6MPH
1056 * 1.9555 * 2.8751 * (G3) 1.556


4th Gear @ 6000 RPM:
6000 * 3.1415 * 24.8
---------------------------------- = 59.0MPH
1056 * 1.9555 * 2.8751 * (G4) 1.333


5th Gear @ 6000 RPM:
6000 * 3.1415 * 24.8
---------------------------------- = 66.2MPH
1056 * 1.9555 * 2.8751 * (G5) 1.190


6th Gear @ 6000 RPM:
6000 * 3.1415 * 24.8
---------------------------------- = 72.7MPH
1056 * 1.9555 * 2.8751 * (G6) 1.083


haha! Confirmed! :thumbup: Speedo was correct!

2nd Gear @ 14,000 RPM:
14,000 * 3.1415 * 24.8
---------------------------------- = 94.3MPH
1056 * 1.9555 * 2.8751 * (G2) 1.947


Plug in the numbers for the variables on your bike and watch the tach! This should tell you pretty close to what your actual speed is!


To get the tires diameter use this!
Remember there are many variables so this is to get us "close"!

********************************************
Using a stock Tire Size of: 180/55 R17
The first number is the Tire's indicated section width in millimeters, measured from sidewall to sidewall. {180}/55R17

Section Width: 180 is converted to inches!
180mm / 25.4 = 7.0866"

Profile or Aspect Ratio: 55
The second number 180/{55}R17 is the tire's aspect ratio or profile.
55% or add a decimal point 0.55

Sidewall Height (SH):
SH = 7.0866" X 0.55 = 3.897"

Wheel Diameter (WD): 180/55R{17"}
WD = 17"

Tire Diameter in Inches:
SH + SH + WD = Tire Diameter
3.189" + 3.189" + 17" = 24.8"

********************************************


I Hope you find this useful! If anyone sees any errors, let me know and I'll correct them! Also I might vote for a Sticky but what section does it belong in??

Regards,
FP

So.....mathematically: What is our top maximum speed with stock everything?
Thanks!

 

[FinalImpact]

I have an Excel spread sheet which you can enter the data into and change all of the variables on the fly if you like. MS Office 2003 version

If someone wants to host it PM me and I'll send it out. My ISP makes this painful to share without giving the whole world my account password.

 

[Nelly]

OK someone really needs a holiday:BLAA:

Nelly

PS of course I'm going to try this. Thanks

 

[Bates121]

So.....mathematically: What is our top maximum speed with stock everything?
Thanks!

Well according to the calculator provided and double checking it with the math provided by finalimpact my top speed is 159.1 MPH @ 14000 rpms I have everything stock except 15 tooth sprocket in front. With a stock 16 tooth front sprocket it is 169.7 MPH@ 14000 RPM

 

[Bates121]

********************************************
Using a stock Tire Size of: 180/55 R17
The first number is the Tire's indicated section width in millimeters, measured from sidewall to sidewall. {180}/55R17

Section Width: 180 is converted to inches!
180mm / 25.4 = 7.0866"

Profile or Aspect Ratio: 55
The second number 180/{55}R17 is the tire's aspect ratio or profile.
55% or add a decimal point 0.55

Sidewall Height (SH):
SH = 7.0866" X 0.55 = 3.897"

Wheel Diameter (WD): 180/55R{17"}
WD = 17"

Tire Diameter in Inches:
SH + SH + WD = Tire Diameter
3.189" + 3.189" + 17" = 24.8"

********************************************


I Hope you find this useful! If anyone sees any errors, let me know and I'll correct them! Also I might vote for a Sticky but what section does it belong in??

Regards,
FP

I think you might have a mistake very minor though
you calculated Sidewall height to be 3.897
Sidewall Height (SH):
SH = 7.0866" X 0.55 = 3.897"

but in your formula you used 3.189. Using 3.189 should have gotten a tire diameter of 23.378 but you got the tire diameter using 3.897 which gives you a diameter of 24.8 like you calculated

Tire Diameter in Inches:
SH + SH + WD = Tire Diameter
3.189" + 3.189" + 17" = 24.8"

 

[Botch]

What we don't know is how much does the tire grow at speed? It does grow some, but I don't know how much!

This should be pretty easy to measure on a dyno (I don't even want to think about how to "calculate" it! )

 

[FinalImpact]

Well according to the calculator provided and double checking it with the math provided by finalimpact my top speed is 159.1 MPH @ 14000 rpms I have everything stock except 15 tooth sprocket in front. With a stock 16 tooth front sprocket it is 169.7 MPH@ 14000 RPM

I doubt the FZ at 96hp will make the number up there. Wind resistance is a factor! And then you have this: The Stock Tire has a Z rating which is good to 149mph with a max speed of (W) = 168mph

My point is this: if the bike was capable in stock trim they likely would have equipped it with a better tire! lol

 

[Bates121]

I doubt the FZ at 96hp will make the number up there. Wind resistance is a factor! And then you have this: The Stock Tire has a Z rating which is good to 149mph with a max speed of (W) = 168mph

My point is this: if the bike was capable in stock trim they likely would have equipped it with a better tire! lol

Very true these numbers are theoretical at this point. Thanks again for the proof I am already playing with the excel sheet i made and am changing variables sprockets and rpm mostly to see what i get.