Designing a Waxless Ski

I don't have accurate data to plug into my math model, but so far the values for coefficient of kinetic friction are very high even when I plug in what I feel would be field accurate assumptions.


What is mass of Skier?70 (kg)
How many meters is the slope?30 (m)
What"s the incline of the plane?45 (deg)
What was the final velocity?45 (m/s)
    4.9293



Here is my math model for designing a waxless ski!


function[muK] = Frictioncoefficient( d,v,G,m )
%Function to calculate the coefficient of friction for any ski
%  Uses change of altitude, and velocity at endpoint


m=input('What is mass of Skier?'); %asks what mass of skier is in Kg
d=input('How many meters is the slope?'); %asks user how big the slope is
slope=input('What"s the incline of the plane?');
v=input('What was the final velocity?'); %What was the
    %final velocity (m/s)?
   
G=9.81; %gravitational constant 9.81m/s^2
h=d*sin(slope);
Fn=m*G*cos(slope);

muK=(.5*m*v.^2-m*G*h)/(Fn*d)




end


This makes me think that I have left an assumption somewhere out of my math model, or I have just not added in all of my data.  Either way, while I know that the values for the coefficient of friction can be above one, the values seem to be inversely proportional to what I might expect.  I would need real data to do testing of my math model to make sure I have errors.

To test this model, I would have to run an experiment at a location that had a constant slope over a specific distance (d), I would need a measurement for initial and final velocity, would need the slope and mass of the skier plus their skis.  With these measured values I should be able to run the experiment.  To get these values I might need a long measuring apparatus, possibly a gps.  An accurate gps might also give me velocity initial and final measurements.  After doing research using an altimeter to tell change in altitude for such a small change seems like it would be fairly inaccurate giving the need for a slope measurement which can be taken with an app using a smartphone.