Why would you need to know the size of the contact patch to use the tyre pressure method? Wouldn't tyre pressure be proportional to the load on the undercarriage (compensating for temp. effects).
Pressure at a given starting weight is 'x'. Add a kilo & pressure is f(x+1). Add 2 kilos & pressure is f(x+2). Add 'n' kilos & pressure is f(x+n).
The relationship could be previously determined using an undercarriage set in a jig.