Ishrub
That's my name ....built like a truck
- Joined
- Feb 18, 2016
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- 8,857
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- Duffy, Canberra, ACT, AUSTRALIA
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- 2x2010 ABS Roadsters, Sprint ST 1050 ABS, 3x250s
Math me please
- Thread starter Claviger
- Start date
Claviger
Aspiring Student
- Joined
- Jul 25, 2014
- Messages
- 6,934
- Location
- Olympia Washington
- Ride
- '21 Z H2, '14 R3R, '02 Daytona 955i
I found a great spreadsheet to do your own calculations on, it all seems to be close to accurate:
All Things (Safety Oriented) Motorcycle - Lean Angle Calculator
All Things (Safety Oriented) Motorcycle - Lean Angle Calculator
1olbull
Riding Motor Since 1950
First separate the questions.
Static lean angle is bike dependent and can be measured . . . carefully.
Dynamic lean angle, no so much, as it involves suspension, rider & weight distribution. Static lean angle would be determined by solving for the tangent of the lean angle, which is equal to the velocity squared divided by the radius times gravity (tan lean angle = v^2 / rg). The "v" is velocity measured in feet per second squared. The "r" is the curve radius and the g is gravity at 32.2 feet per second per second.
What Rob has shown is a chord bisecting an arc portion of a radius. A chord should be measured within the tangent points of a curve on the center line. A middle ordinate is measured at 90° from the middle of the chord out to the arc (centerline). Radius of the curve is then determined by r = C^2/8M+M/2.
There is chassis lean angle and effective lean angle & they are NOT the same. The effective lean angle is a line from the center contact patch through the CM (center mass of the motor and rider). The lower the combined CG the less the lean angle. That is why a rider hanging off the seat to lower his CM, results in a lowering the combined CG and results in less lean angle and more clearance for the motorcycle.
The tangent of the lean angle equals the necessary friction value to maintain traction. Most dry level roadways produce about .75g friction value. Exceed this and you be on yer butt! Some tire rubber produces more friction; however, on a public roadway the difference is mitigated and negligible for our purposes.
Gotta go - more later if there is interest . . .
Static lean angle is bike dependent and can be measured . . . carefully.
Dynamic lean angle, no so much, as it involves suspension, rider & weight distribution. Static lean angle would be determined by solving for the tangent of the lean angle, which is equal to the velocity squared divided by the radius times gravity (tan lean angle = v^2 / rg). The "v" is velocity measured in feet per second squared. The "r" is the curve radius and the g is gravity at 32.2 feet per second per second.
What Rob has shown is a chord bisecting an arc portion of a radius. A chord should be measured within the tangent points of a curve on the center line. A middle ordinate is measured at 90° from the middle of the chord out to the arc (centerline). Radius of the curve is then determined by r = C^2/8M+M/2.
There is chassis lean angle and effective lean angle & they are NOT the same. The effective lean angle is a line from the center contact patch through the CM (center mass of the motor and rider). The lower the combined CG the less the lean angle. That is why a rider hanging off the seat to lower his CM, results in a lowering the combined CG and results in less lean angle and more clearance for the motorcycle.
The tangent of the lean angle equals the necessary friction value to maintain traction. Most dry level roadways produce about .75g friction value. Exceed this and you be on yer butt! Some tire rubber produces more friction; however, on a public roadway the difference is mitigated and negligible for our purposes.
Gotta go - more later if there is interest . . .
Claviger
Aspiring Student
- Joined
- Jul 25, 2014
- Messages
- 6,934
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- Olympia Washington
- Ride
- '21 Z H2, '14 R3R, '02 Daytona 955i
Steve comes in a blows my mind in 10 lines lol. Wish I'd payed attention in geo/trig!! The calculator I linked provided a return of the below:
Meaning, I kept around 7 mph as a theoretical reserve before washing out. Just trying to wrap my head around margins before washing the front or low siding from the back.
Meaning, I kept around 7 mph as a theoretical reserve before washing out. Just trying to wrap my head around margins before washing the front or low siding from the back.
TXtriple
SIC VIS PACEM PARA BELLUM
I have no idear what y'all are talking about. And Bull...you must've stayed at a Holiday Inn!
Claviger
Aspiring Student
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- Jul 25, 2014
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- 6,934
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- Olympia Washington
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- '21 Z H2, '14 R3R, '02 Daytona 955i
Honestly, I don't know many people who have the mastery of Trig he has. It's **** impressive.
TheKid
Top Fuel
- Joined
- Feb 2, 2011
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- 1,919
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- Dry Ridge Ky, USA
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- 2007 Rocket III Standard /2010 R3T
The engine sits so high on these things. That has a lot to do with it, I think.
I know that my Touring, will (would have) handled better than my 07 Standard. I believe it is because the Touring has a more narrow tire. This is also why I have been wanting to make it a Cafe Racer(pipe dream)
I know that my Touring, will (would have) handled better than my 07 Standard. I believe it is because the Touring has a more narrow tire. This is also why I have been wanting to make it a Cafe Racer(pipe dream)
Claviger
Aspiring Student
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- Jul 25, 2014
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- Olympia Washington
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- '21 Z H2, '14 R3R, '02 Daytona 955i
While the engine is indeed high, a higher CoG reduces required lean angle, crazy right?
Higher CoG gives you a bigger effective lever on CoG and means it must move a lesser distance for drastic effect.
My hypothesis is that the CoG is MUCH lower than you'd expect from looking at the bike. Front to rear is also not what you'd expect from looking at it.
For my bike, the CoG from front to back is 46" from the rear most point on the bike, on a total vehicle length of 93". That's 31" forward of the rear axle with a wheelbase of 65" (actual measurement), yeilding a 53/47 weight distribution that's actually FORWARD biased. Crazy right?
CoG found using jacks along the foot board rail, I was curious lol.
That all changes with a rider mounted, as the seat is wholly located behind the CoG, so it will shift rearwards significantly. I worked it out mathematically last night, came up with 53.6 Rear / 46.4 front when I’m sitting up in the saddle.
Higher CoG gives you a bigger effective lever on CoG and means it must move a lesser distance for drastic effect.
My hypothesis is that the CoG is MUCH lower than you'd expect from looking at the bike. Front to rear is also not what you'd expect from looking at it.
For my bike, the CoG from front to back is 46" from the rear most point on the bike, on a total vehicle length of 93". That's 31" forward of the rear axle with a wheelbase of 65" (actual measurement), yeilding a 53/47 weight distribution that's actually FORWARD biased. Crazy right?
CoG found using jacks along the foot board rail, I was curious lol.
That all changes with a rider mounted, as the seat is wholly located behind the CoG, so it will shift rearwards significantly. I worked it out mathematically last night, came up with 53.6 Rear / 46.4 front when I’m sitting up in the saddle.
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This about tells the whole story. Keep in mind that the contact patches on the tires move towards the center of the curve relative to the center of gravity. (See Rob's post above.) With the wide rear tire on the R3 this contact moves further inward than the front contact patch. This does two things: it moves the contact patch closer to the center of gravity so the bike wants to return to vertical, and it changes the tangent line of the direction of travel relative to the curve radius. The cumulative affect is the bike moves wide thus requiring ever greater rider input to maintain the intended line.
R3T riders comment on how the touring turns easier. It does in part because of the narrower rear tire. Put a 10" wide rear tire on your favorite sport bike and it will handle much more like the Rocket.
BillyIndiana
Road rash heals-Freckles grow back-Ride
I understand what you are asking, but what is the real world application? If you are trying to improve the overall performance of the handling I get it. The only other application is if you are looking at doing track time on a laid out coarse that makes sense too.
In real world applications there are too many variables and unknowns to take into account. One of my favorite features of my R3T is how well it performs for such a big bike, but it makes you work for it for sure. It takes steady nerves to throw these bikes low into the corners and then power out. It is one of the things that separates those of us that ride these bikes.
I get around my cruiser friends and most of them have no understanding of how well their bikes perform. Until they head someplace like the Dragon for the first time and get the bejesus scared out of them.
PS I hope you are wear full leathers doing this stuff.
In real world applications there are too many variables and unknowns to take into account. One of my favorite features of my R3T is how well it performs for such a big bike, but it makes you work for it for sure. It takes steady nerves to throw these bikes low into the corners and then power out. It is one of the things that separates those of us that ride these bikes.
I get around my cruiser friends and most of them have no understanding of how well their bikes perform. Until they head someplace like the Dragon for the first time and get the bejesus scared out of them.
PS I hope you are wear full leathers doing this stuff.
