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jg
Augusta, ME
USA
272 Posts |
Topic started on 05/06/2004 at 2:13:02 PM
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** I have revised this post to fix some typos and update with better information. I found my initial estimate of the drag coefficient of a dirt bike may have been a little high. I have read that motorcycles have drag coefficients in the range of 0.6 to 1.0. Sport bikes have drag coefficients of around 0.6. Dirt bikes would be on the higher end. I will now use 0.95 for my estimate.**
You can calculate theoretical top speed for any bike, but you have to do a couple important estimations, namely, the projected frontal area of the bike and rider and the drag coefficient. You can use a frontal picture of yourself seated on your bike and a ruler to help estimate area by scaling everything.
The drag force on a bike & rider is:
F = (1/2)(rho)(V²)(A)(Cd)
Where
F is drag force (Newtons)
rho is air density (kg/m³), about 1.2 kg/m³ at sea level
V is velocity (m/s)
A is projected frontal area of bike and rider
Cd is drag coefficient (dimensionless). A dirt bike will be on the higher end of range of typical drag coefficients for motorcycles (I will use 0.95). Things like fenders, shrouds, helmets without full face shields, loose jackets, etc. all create little pockets that can increase the drag coefficient. For example, an anemometer with hemispherical cups spins because the drag coefficient for air blowing into the cup is about 1.4 and the drag coefficient for air blowing around the outside of smooth hemisphere of the cup is about 0.4.
The power required to maintain a given speed is the drag force, F, multiplied by the velocity.
P = F · V
P = (1/2)(rho)(V³)(A)(Cd)
Where
P is power (Watts).
745.7 W = 1 horsepower
For example, I will use my bike:
My XR350 can produce about 30 or so horsepower (although Honda claims 31.8 horsepower), or about 22,371 Watts. Horsepower at the rear wheel would be the best number to use, since this would take drivetrain friction out of the picture. I estimate around 0.7 m² projected area, and a drag coefficient of 0.95.
22,371 W = (1/2)(1.2 kg/m³)(V³)(0.7 m²)(0.95)
V = [(22,371 W)/(1/2 · 1.2 kg/m³ · 0.7 m² · 0.95)]^(1/3)
V = 38.27 m/s = 85.6 mph (1 m/s = 2.2369 mph)
This means my bike should have enough power to propel me up to 38.27 m/s, which is 85.6 miles per hour. According to my shop manual, my engine produces peak horsepower at 7000 rpm. I need to gear my sprockets so that my engine's power peak at 7000 rpm will occur when the bike hits 85.6 mph in sixth gear. There is a gearing calculator in the tech section called Top Speed (or you can do it by hand).
You can enter your rear tire outer diameter and transmission ratios. Then, the remaining variables that determine speed are sprocket gearing and engine rpm. For my bike, I would use 7000 rpm and work out what sprockets I needed to use to hit 85.6 mph at that engine speed in sixth gear. This should be a good starting point towards gearing the sprockets for maximum top speed capability. Minor changes in sprocket gearing, either up or down, will probably be needed for the very best speed.
As an alternative to make things quicker, here is chart I made showing Horsepower To Overcome Drag vs. Speed, at an air density of 1.2 kg/m³. Use the line that is the closest match for the product of your projected frontal area and drag coefficient, or interpolate for more accuracy:
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1984 XR350R
See pics here: Honda XR350R Category |
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DanDog
95 XR600R
USA
272 Posts |
Posted on 08/17/2004 at 2:06:47 PM
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Maybe I am missing something. But I can not see were the drag has any effect on the top speed of any of my dirt bikes? (assuming: traction > drag)
My reasoning is that dirt bikes have alot more power than gears. For example, my Honda XR600R on a 'paved road' will run out of 5th gear about 1/2 throttle. According to 'topspeed' calcs thats 97 mph.
I have to guess. But I think that bike has around 60 HP.
I drive s-california freeways occasionally on the bike. So i use a 15/48 sprocket and a 25.5" tire.
My next rear sprocket will be a 40 tooth. But I would be suprised if my top speed was drag limited even then.
Am I missing something?
Thanks
Dan
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bp 1.8
Bemidji, MN
USA
106 Posts |
Posted on 10/29/2004 at 10:32:26 PM
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i think the numbers are off. i can do 80 on a chinese copy of a honda dirtbike with a 125cc stock engine after putting an appropriate sprocket on it.
if a little 125 chinese clone engine can do 80 youre 350 should do alot better than that with the right sprockets. |
Panterra 125 |
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Honda152
S Portland, ME
USA
165 Posts |
Posted on 01/16/2005 at 09:38:06 AM
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| i doubt any 125 is going to go 80 unless it's a race bike (ie CR 125, YZ 125, KX, RM, SX) |
2005 CRF250R, 2006 CRF450R, 2004 CRF50F |
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Woody Racing
Sammamish, WA
USA
259 Posts |
Posted on 01/26/2005 at 5:04:44 PM
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| wow you want to do my physics homework when i take it next year. (or any of my math) |
Bikes: 2003 CRF230F, 2002 XR100R (For sale) |
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Pappy
Smithville, Ont
Canada
113 Posts |
Posted on 02/10/2005 at 4:40:27 PM
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| um dont understand any of that man |
03 XR100R |
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FreeMe
Portland, OR
USA
47 Posts |
Posted on 02/17/2005 at 10:31:19 AM
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I am impressed with the math here, but I'm the wrong kinda geek to have the patience to use it.
For an easy real-world method of finding the actual top speed of your dirt bike, there is no better way than carrying a GPS (somewhere high on your body, for good reception) and checking the max speed stats after a ride across level ground. GPS units are extremely affordable now (some for as little as $80), which makes them a justifiable adition to your trail riding gear.
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TT-R225 |
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Pappy
Smithville, Ont
Canada
113 Posts |
Posted on 02/18/2005 at 11:57:57 AM
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umm or u could do this V=d/t
t is time and d is distance and u find out the distance and the time it took u 2 do the ditance and u divide d/t and then u will have ur speed some thing like that haha pappy ant that stupid |
03 XR100R |
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FreeMe
Portland, OR
USA
47 Posts |
Posted on 02/18/2005 at 12:33:02 PM
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| Yep - you could do it that way, but it would only be accurate and consistant if you used triplights (electric-eye switch) over a measured distance. You COULD be reasonably accurate if you had two guys with synchronized stopwatches standing at beginning and end of a measured mile - but that's the hard way anymore. |
TT-R225 |
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Marc Salvisberg
California
USA
1 Posts |
Posted on 08/12/2009 at 11:46:42 AM
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jg,
I know that this is ancient, but, did you ever consider that your HP was a lot lower than 30?
Marc |
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madmac650
Sultan, WA
USA
88 Posts |
Posted on 08/13/2009 at 06:53:35 AM
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| WOW! Got some spare time between shuttle missions, eh? well I know who to talk to next time I want to launch my own sattelite into orbit, or get shot out of a cannon. |
2005 XR650L - Dave's mods, Keihin 55/Mikuni 165, 1.75 turns, uncorked, Uni air filter, IMS smog block, de-snorkeled, de-boogered stock header, Jetson CZR, IMS 4.0 gal tank, vented "baja" fender mod, XRs only temp dip stick, growl's oil cooler, relocated horn. |
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Sanosuke
World Traveler
Canada
638 Posts |
Posted on 08/14/2009 at 12:59:46 PM
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Derviatives are the key to the trick here... :) The second derivative of the equation yields the slope of the line. Now I've done someone's calculus homework, can I have my $50 please? ;)
Sanosuke! |
2007 Wolverine 450
2004 XR250R - BC Canada XR250R
Donated to the support of 4Strokes.com |
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HorseRider650
Ohio
USA
552 Posts |
Posted on 08/14/2009 at 1:11:58 PM
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Sanosuke, glad to see you back and OK |
08 XR650l - Big Red Elephant
10 KTM300XC-W - Just Orange
09 KX85 - Son's MX ride (AKA: The Weed Wacker)
07 CRF80 -Son's trail ride.
08 XT250 - lil_mynx
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Topic |
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Calculating the top speed of a dirt bike
