Yours is one of the all-time classic, non-trivial "Physics of Skiing" questions. The first time I ever saw it discussed on the internet was in 1995. For your amusement, take a look at the first post in the thread http://tinyurl.com/y36f
and browse forward through the entire 188 posts. Unfortunately, this RSA thread contains a lot of misconceptions, errors in elementary physics, as well as out-and-out silliness, so its not particularly useful, except in terms of providing examples of the the type of errors and misconceptions that can be made in such a discussion. Similar threads regularly appear in many ski forums.
I believe there was a fairly good thread on this subject here on Epic a year or two ago, but with the poorer search engine of Epic compared to Google, I couldn't lay my hands on it at the moment. As I recall, one writer in the EpicSki thread took the emperical approach and simply looked at the undebateable historical evidence to see whether heavier or lighter racers tended to win in the various events (ie, DH, SG, GS, SL). I think I remember the conclusions, but hopefully someone will be able to provide the URL of that thread and the real numbers.
Even the seemingly simple theoretical situation of sending two weighted, riderless, identical skis down a hill has substantial complications. In a vacuum, and with no friction from the snow, they clearly would both arrive at the bottom of the hill at exactly the same time, no matter how steep the hill, or how much weight each was carrying. On the other hand, in the real world, the arrival times will depend on the weight they carry because the several forms of friction acting on them depend on weight in quite different ways. Some are independent of weight (eg, aerodynamic drag), some increase with weight, and some decrease with weight, everything else (slope angle, ski and base prep, etc.) held constant.
For example, on a shallow slope covered with deep powder, the ski with the heavier weight will indent the snow more and might even get completely bogged down, whereas a ski carrying a very light weight would tend to ride on top of the snow and have not only less total friction, but also less relative friction (ie, frictional force divided by the skier's weight - like a psuedo coefficient of friction).
Another situation: On cold, packed, abrasive snow, the extra weight carried by the heavier of the two skiers skier might provide enough down-the-hill force to break his skis free (ie, overcome the "stiction"), whereas the lighter skier on the same slope might only have barely enough down-the-hill force to break free, and so will accelerate more slowly and have a lower terminal velocity.
As a final example, at very high speeds, wind resistance is often the dominant factor, so, assuming the heavier skier and lighter skier have approximately the same frontal area in a tuck, their aerodynamic friction would be the same, so the heavier skier will reach a higher terminal velocity.
Real skiing situations are more complex than the above "ideal" cases, and also involve the muscle power and skill of the skier, so the real answer to your question must always be empirical, from the historical record (as mentioned above). I'm pretty sure I remember the "answer", but hopefully, someone will post the link or equivalent data.
Tom / PM[ December 08, 2003, 03:53 AM: Message edited by: PhysicsMan ]