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What's wrong with this 'speed in gear' formula?
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Posted by: zag
Hi Engineering Guys,
I've been trying to figure out the potential mph for a bike in a given gear and final drive ratio. The formula I came up with starts with crankshaft(tach) revolutions per minute, converted to per hour, then to revs/hr at the sprocket (gearbox output shaft revs), then to wheel revs/hr, then to wheel distance travelled/hr:
mph = T [Tach] engineRev 60 min
------------------- * ------
1 min. 1 hr.
E [engine]teeth gbOutRev
* --------------- * --------------
engineRev O [gbOut]teeth
S [sprocket]teeth wheelRev
* ----------------- * --------------
gbOutRev C [wheel]teeth
D" tireDiam * 3.14 mile
* ------------------ * --------------
wheelRev 63360 inches
0.002973*T*E*S*D
or mph = ---------------- D in inches
O*C
key: gbout = gearbox output shaft
rev = revolutions
Data for the example:
O / E
| |
V V
Gear ratios:
----WR250F--------------YZ250F-------
1st 31/13 (2.384)__ 1st 30/14 (2.143)
2nd 28/16 (1.750)__ 2nd 28/16 (1.750)
3rd 28/21 (1.333)__ 3rd 29/20 (1.450)
4th 25/24 (1.042)__ 4th 27/22 (1.227)
5th 22/27 (0.814)__ 5th 25/24 (1.042)
Sprocket/Chainwheel:
S/C 13/52 13/48
Assuming a rear tire carcass diameter of 24", I get 13,500rpm in 5th on the WR is 300+ mph. Clearly, I ain't in the ballpark. Can someone clue me in on where I went wrong? Ideally I'd like more than the correct formula; what was wrong with my logic on this?
Obviously, I'm leaving out wheelspin, tire growth, circumference difference when on hard-pack, etc.... I'm just trying to see how much the WR transmission alters the speed range of the bike.
Thanks in advance for your help.
Allen
Posted by: RM_guy
So YOU are the one with the fastest bike ever made!!! http://dirtrider.net/ubb2/tongue.gif
------------------
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Ah,um...Sure did. I was right behind you!
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Posted by: Rich Rohrich
This may shed a little light.
http://www.ericgorr.com/mototech/mo..._march_2000.htm
------------------
Rich Rohrich
==
"Wisdom is not a product of schooling but of the life-long attempt to acquire it."
- Albert Einstein
Posted by: zag
Doh!
Tried to format the formula with blank spaces, and it all got eaten by the bbs poster!
So much for WYSIWYG.
Thanks Rich for the link. It definitely helped. It looks like I left out one piece - the primary reduction. I guess I need to post to Thumper Central to see if any of the Yamaha guys have it in a manual.
Eric's mototech page implies a typical primary reduction of about 3:1, and a tire circumference of 84". Changing my formula and formatting so hopefully it posts ok, and using the (hopefully)correct terminology:
mph =
R*E*S*D*T*0.02975
-----------------
L*O*C
where:
R=Primary reduction crank gear
L=Primary reduction clutch gear
E=Internal reduction main(clutchshaft) gear
O=Internal reduction countershaft gear
S=Final reduction sprocket gear
C=Final reduction chainwheel gear
D=Diameter of the tire in inches
T=Engine crankshaft RPM
constant= 60 minutes * 3.14159 (circumference is pi*D) /(12inches*5280ft)
Testing the example in the link produces the same 88mph top speed @ 11,000rpm result.
With the data for the WR250F in 5th gear at 13,500rpm redline, assuming:
- 26.74" tire diameter
- 3:1 primary reduction
mph = 1*27*13*26.74*13,500*0.002975
/(3*22*52)
= 109.8 mph
Makes me wonder what a real-world top gear maximum rpm would be, and the correct primary reduction ratio...
Thanks, Rich.
curious Allen
Posted by: wrench
ZAG,
2001 Yamaha WR 250F
From the manual [General Specifications pg.2-2].
Primary reduction ratio = 57/17 (3.353)
Secondary reduction ratio = 53/13 (4.000)
Gear ratio =
1st-31/13 (2.385)
2nd-28/16 (1.750)
3rd-28/21 (1.333)
4th-25/24 (1.042)
5th-22/27 (0.815)
Hope this helps
wrench
Posted by: zag
Thanks, Vince.
For those who're interested, I've put this formula into a spreadsheet, with the YZF and WRF data in it. It lets you play with final drive sprocket selection & tire size, and shows the results in mph at four rpms. If you know Excel, it could easily be adapted to other bikes' info. It's in Excel, email me if you want a copy.
fyi
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