Snow Goer November 2024 | Page 48

BY T . J . KROB

The Math Behind Ski Stance

Modern snowmobiles are equipped with all sorts of fancy technology these days . Examples include giant digital screens , heated seats , on-board navigation , self-adjusting shocks , case-specific tracks with monster lugs and general designs that employ many exotic and expensive techniques . It ’ s all done to make our lives even more fun in the winter .
Despite these advancements , modern sleds – whether dedicated for riding trails or mountain sides – still have many common , unchanged principles or design qualities that they ’ ve utilized for quite some time . For instance , sleds come with one track in the rear for propulsion and two skis up front that are set underneath spindles and suspension .
There have been advancements in shock absorbers , intense geometry changes to make sleds handle better and more in the evolution of the front end of a snowmobile . But one fact still remains : The two skis on the snow are separated by a case-specific distance – the ski stance .
Most folks know that ski stances vary , ranging from trail ( usually the widest ) to crossover ( a little narrower ) and mountain ( usually the narrowest ). Utility-focused sleds have been up and down the ski stance spectrum .
The trend of mountain sleds becoming narrower has been adopted by each manufacturer . Stances that used to be around 42 inches wide dropped to 40 inches , then to 38 and now hover in the 34- to 36-inch range . Conversely , trail sleds have increased in width from the old standard 38 and 40ish inches to now reaching about 43 inches wide . ( Or , if you ’ re overseas on a Lynx 59 Ranger , you could be riding a sled with a whopping 59-inch stance .)
So what ’ s the science behind it all ? A generalization would be that a wider sled is more laterally stable , meaning it absorbs more force applied laterally , than narrower ones . In the 1970s , the Snow Goer test team at the time demonstrated the effect by using a rollover tilt table to measure the angle at which each snowmobile ' s upper ski began to lift . Typically , the wider the stance , the higher the tipping point .
Mathematical concepts found in statics ( which is rooted in physics ) in the mechanics education realm describes the behavior of physical systems when they are subjected to forces . The basic idea in statics is the equilibrium of forces , where no acceleration in any direction occurs – meaning the summation of forces and moments acting about an object must remain at 0 . ( Jumping into the next stage where objects move in space is another area of study known as dynamics .)
Assessing the amount of force required to tip a snowmobile up onto a single ski can be isolated using a few equations . Of course , a perfect physics world assuming many constant variables and perfect “ spheres ” or blocks is required to wrap one ’ s head around a few ideas , but the extrapolation and overall science illuminates the impact an inch one way or another may have on the
As the pushing force increases on the box , it will either begin to slide along surface ( slipping ) or it will begin to rotate . ( tipping ) overall riding experience .
Picture doing some typical in-garage maintenance where you need to tilt the sled up onto one ski to change a ski ’ s carbide runner . You push sideways on the handlebar to make the sled tip up onto one ski . Slipping versus tipping is partially the principle depicting how much force is required to make the sled lean or tip . ( Big caveat : Yes , when we ’ re riding , we can weight-bias a machine with our body weight / positioning through the running board , which is a partially off centerline axis to one side , which in turn changes a sled ’ s center of gravity by squatting the shock slightly , etc . So , the math in this example is isolated to an at-rest , static case where perfect physics world happens .)
Enter the math and the statics . Free body diagrams illustrate the forces and moments placed on an object along with their spec dimensions .
First consider the force of the body pushing down on the earth . This is equivalent to weight in a different unit where F = m * a ( force = F , m = mass , and a = the acceleration due to gravity ). In metric units , F is expressed in Newtons ( kg * m / s2 ), while Imperial is pounds ( slug * ft / s2 ).
Moments are created when pushing on an object with an offset from center , creating turning about an axis equaling the magnitude of force multiplied by the offset distance from the center . By summing the moment of the snowmobile ’ s weight at its center versus the force exerted laterally at the skis point of contact at the ground , we isolate the force needed to tip – and the effect of in-
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