Counter-steering: Lean-angle force dynamics -- test data from Valentino Rossi

September 30, 7:19 PMDC Motorcycle Travel ExaminerMark Poesch

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Motorcycling 101: Counter-steering essentials shows the derivation of the idealized equation for the relationship between speed, lean angle, and turn radius:

Radius = Speed^2 / ( Gravity * Tangent( CG Lean Angle ) ) 

The series Counter-steering revisited: Redux -- how it works, discusses how the force causing acceleration into the turn, and balancing torques -- again, idealized -- interact to enable a motorcycle to turn.  The question left unanswered is: How close to the real-world are these equations?

With seven laps remaining, on board with Valentino Rossi at his home track in San Marino, we get the test data.  The telecast shows the bike’s lean angle, and telemetry for the bike’s RPM, gear, position on the track and speed.  Satellite imagery of the track provides the final component: an approximate measurement of the radius Rossi is following through each turn.

Yamaha's Valentino Rossi of Italy, right, is chased by the Honda of third placed Daniel Pedrosa, of Spain, and by Yamaha's Jorge Lorenzo of Spain, second placed during the San Marino MotoGP at the Misano circuit, in Misano, Italy, Sunday, Sept. 6, 2009. (AP Photo/Gregorio Borgia)

Rossi’s body position (a significant factor affecting the effective lean angle of the combined CG) is neglected in this analysis.  However, so are a host of other factors including: front/rear tire slippage, front/rear tire tracking radii, lean angle adjustment for contact patch offset from the central bike axis, front/rear weight distribution, etc.

What we see in turns six, eleven and twelve is Rossi’s body-position nearly perfectly canceling all the other factors excluded from this equation, enabling him to achieve a nearly perfect theoretical minimum radius for the speed and lean angle he rode.

Readers are invited to speculate in the comment section below about the variance from the theoretical minimum in the other seven turns measured.

For more information:
- Counter-steering revisited: Redux -- how it works
- Counter-steering -- how it works: Part 2 -- force causing acceleration
- Counter-steering -- how it works: Part 3 -- balancing torques
- Counter-steering -- how it works: Part 4 -- lessons learned
- Counter-steering -- how it works: Part 5 -- lean-angle force dynamics