Editing Countersteering (section)

===Need to lean to turn===
A bike can negotiate a curve only when the combined [[center of mass]] of bike and rider leans toward the inside of the turn at an angle appropriate for the velocity and the radius of the turn:

:<math>\theta = \arctan \left (\frac{v^2}{gr}\right )</math>
where <math>v</math> is the forward speed, <math>r</math> is the radius of the turn and <math>g</math> is the acceleration of [[gravity]].<ref name="fajans" />

Higher speeds and tighter turns require greater lean angles. If the mass is not first leaned into the turn, the [[inertia]] of the rider and bike will cause them to continue in a straight line as the tires track out from under them along the curve. The transition of riding in a straight line to negotiating a turn is a process of leaning the bike into the turn, and the most practical way to cause that lean (of the combined center of mass of bike and rider) is to move the support points in the opposite direction first.<ref name="Wilson">{{cite book
| title = Bicycling Science
| edition = Third
| last = Wilson
| first = David Gordon
| author2 = Jim Papadopoulos
| year = 2004
| publisher = The MIT Press
| isbn = 0-262-73154-1
| pages = [https://archive.org/details/isbn_9780262731546/page/270 270–272]
| url = https://archive.org/details/isbn_9780262731546/page/270
}}</ref>