Which Way Did the Bicycle Go?

Solution Method from Which Way Did the Bicycle Go? by Konhauser, Velleman and Wagon,published by the MAA, 1996

Imagine that while walking down a dirt path, you see the following pair of tire tracks that you guess were made by a bicycle. Can you determine which way the bicycle was going?

*Some useful assumptions about bicycle tracks* The distance between the points of contact of the two tires and the ground is a constant. The back tire is fixed in the frame. This implies that the line connecting the front tire's position at time t and the back tire's position at time t is tangent to the back tire track. From riding bicycles, one may deduce that the front tire should oscillate more than the back tire, that is of the two tracks the one on the outside should be the front tire track. [This may be proved from the first two assumptions.]
See An Animation of a Bicycle Creating a Track
Procedure to Determine the Direction the Bicycle Was Going Use the third assumption about bicycle tracks to determine which is the front tire track and which is the back tire track. Choose a few points on the back tire track and draw the tangent lines at these points. For each chosen point on the back tire track B, identify the first point to the right and to the left where the tangent line intersects the front tire track . Call the point to the right R and the point to the left L. Measure the lengths of the line segments BL and BR, for different choice of the point B. The bicycle is going in the direction for which the length is constant, as per the first assumption about bicycle tracks.

Some useful assumptions about bicycle tracks

The distance between the points of contact of the two tires and the ground is a constant.
The back tire is fixed in the frame. This implies that the line connecting the front tire's position at time t and the back tire's position at time t is tangent to the back tire track.
From riding bicycles, one may deduce that the front tire should oscillate more than the back tire, that is of the two tracks the one on the outside should be the front tire track. [This may be proved from the first two assumptions.]

See An Animation of a Bicycle Creating a Track

Procedure to Determine the Direction the Bicycle Was Going

Use the third assumption about bicycle tracks to determine which is the front tire track and which is the back tire track. Choose a few points on the back tire track and draw the tangent lines at these points. For each chosen point on the back tire track B, identify the first point to the right and to the left where the tangent line intersects the front tire track . Call the point to the right R and the point to the left L. Measure the lengths of the line segments BL and BR, for different choice of the point B. The bicycle is going in the direction for which the length is constant, as per the first assumption about bicycle tracks.