Tire Heating on Landing, Part 2

In the last post, we talked about the moments of sliding/rolling motion when a tire first contacts a surface with a mismatched velocity.  Using the assumptions and simplifications outlined in that post, today we will make estimates of heat generation at the tire/runway interface, and temperature profiles inside the tire material based on a hypothetical airplane landing scenario.

It was assumed that we were provided with the instantaneous forward velocity of the wheel axle, the instantaneous rotational velocity of the wheel, the horizontal force at the wheel axle, and the contact area of the tire.  Using this data, an instantaneous sliding velocity is easily calculated.  Then conservation of energy dictates the instantaneous rate of total energy generation at the sliding interface.  Using the assumptions outlined in the last post, an imposed heat flux into the tire can be estimated as a function of time.  

The blue line in this figure shows the instantaneous heat flux into the tire. 
 Since the tire is rolling (with increasing rotational velocity) the same area doesn’t stay in continuous contact with the runway. 
 

The contact time for successive points are shown in this figure.  As point “E” lifts away from the runway at about 80ms, full rolling motion is achieved and there is no more sliding contact, and hence no more heat generation from sliding friction.  Returning to the previous figure, each of the horizontal black lines represents the average heat flux  over the period that each of the indicated points is in sliding contact with the runway.
Using the average heat flux for points A-E, the temperature rise of the tire can be calculated.  

 

This figure shows the temperature as a function of distance into the tire for at point “A” for five different times starting at 0.5 ms after touchdown, and lasting until the rolling motion of the tire has “A” lifting away from the runway.

This figure shows the temperature history of “A” from touchdown to 8.7 ms at four different depths.  At these very small timescales, the penetration of the heat is very shallow, justifying the assumption of modeling the heat flow as occurring in a semi-infinite solid.





 
This figure shows the surface temperature rise for each of the 5 points indicated in the first figure over the full 80ms duration until pure rolling motion begins.










Based on this approximate analysis of hypothetical but reasonable data, it can be concluded that frictional heating from sliding can cause the surface temperature to rise very high even in the short contact times involved, the temperature rise occurs in a very thin layer near the surface, and that the heat flux peaks early and falls off quickly as the tire rolling velocity increases.