# What is the Davis Equation and why is it used in a Train Simulator?

I have been trying to understand how Microsoft Train Simulator works and people seem to use some Davis equation to calculate friction. So my questions are: What is it? Why do they use it? Are there alternatives to calculate train friction/are there other ways to calculate train friction?

Basically, the Davis Equation is a resistance formula mainly used in basic go-stop situations like trains. The basic formula: $$R'=1.3+\frac{29}{w}+.045v+\frac{.0005av^2}{wn}$$ R being resistance, w is axle load in short tons, n is the number of axles, and a is the frontal area of the train in sq. feet. According to Szanto in Rolling Resistance Revisited you can modify the equation to fit standard freight cars, but the concepts are the same, factoring in air resistance as well. When you or the simulator substitutes the values above to yield certain necessary values for the simulation, you can find relatively accurate coefficients of drag. When you get resistance/drag the simulator will then compute whatever other factors are necessary and then create the appropriate image. This (according to Microsoft Train Simulator) happens hundreds of times a second at the highest settings to give high quality data for the discerning user. Now as to your third question, yes, there are other ways of calculating friction, but the Davis Equation was designed specifically for this purpose and requires no extraneous values and in a sense is the most 'streamlined' equation for this purpose. Some come close though, most prominent being the Canadian National modification for double deck EMU's: $$R=14*\sqrt{10(M)(n)}$$ This square root function will yield more accurate resistance coefficients for taller wagons. If anybody has found more accurate and EFFICIENT methods of finding resistance for trains than the Davis please edit or answer thusly, but as to my point of view the Train Simulator, as with all computer programs, uses this equation to balance both accuracy and speed of calculation.