Gravity Theory..

[Dave Winters]

 

O.K., this has probably been discussed before, and maybe should be on the Racing forum, but it's been bugging me for years.

So, the question is, does a heavier rider have an advantage in a race regardless of ability and wax. I say this is a myth.

Theoretically, now: two riders, same ability, boards and wax. One weighs 130 lbs and one weighs 230 lbs. Does the heavier rider reach the finish faster?

Physics 101 says no ( I think). We'll go back to the 16th century when Galileo dropped two balls the same size but different weights off the leaning tower of Pisa and they hit the ground at the same time.

In fact, I would say the lighter rider would have an advantage due to less wind resistance!

Now, bigger athletes have bigger, stronger legs and can pump out of turns more powerfully, that's not part of this discussion.

What do y'all think?

[st_lupo]

This has always confounded me too, but my quick, shoot from the hip (no racing) take is: heavier riders do have an advantage.  You see this practically on the slope and in theory.  You even see this in Galileo's experiment.  NASA, in fact has a wonderful experiment where they drop a bowling ball and a feather in an evacuated chamber.  Boom! Both hit the ground at the exact same time! Wonderful!  But in everyday life, we know the bowling ball will drop faster, precisely because (like you mentioned) drag plays a factor.  Given to identically shaped objects, your drag force is going to scale based on the cross sectional area, Your inertial force is going to scale with the mass of the object.  For simplicity we examine a sphere (other objects roughly follow this).  A sphere's cross sectional area scales with the square of the radius (r^2), whereas the mass scales with the cube of the radius (r^2), so when working out the equations of motion, the the inertial component (helping to _maintain_ speed) is going to grow faster than the drag forces (working to reduce speed) as a function of size.  Additionally, the drag force is going to grow with the square of the riders speed, becoming increasingly important (and differentiating) at higher speeds.

The ideal candidate would actually be a _denser_ rider: small rider (low drag) with a lead belt (high inertial forces).

One thing that does work in the lighter rider's favor is the drag of the snow on the board, which is proportional to the rider's mass.  But I'm not sure of the magnitude of that force relative to aerodynamic drag.

[Odd Job]

I am willing to donate fat, if it will help your son.

#fatfortheflats

[charliechocolate]

Have Cody load up on dairy queen ice cream cakes and find out.

[st_lupo]

Highly simplified highschool math follows…

(forgive the handwriting, decades behind a keyboard has destroyed what little handwriting skills I had to begin with )

[TimW]

Also depends on the shape. For the same weight the tall skinny guy will lose out the the short stubby guy. Beer helps.

BMI is calculated relatively to your length squared. So apparently human mass does not increase with you length the the 3rd power but its closer to your length squared.

Human frontal area might also not increase with your length squared (as one would expect) but a bit less. I think tall people do no increase in width proportionally (I can serve as anecdotal evidence for that).

 

 

[st_lupo]

Absolutely, but then the drag coefficient becomes a variable and the math becomes a lot less clear.  Just found this link: https://www.scirp.org/journal/paperinformation.aspx?paperid=76068  that attempts to statistically correlate various body-type parameters with skiing performance.  (Warning: tons and tons of jargon that goes beyond me).  It could be confirmation bias but a couple of sentences stand out:

>>>

Irrespective of gender, skiers specialized in TECH events differed in anthropometric data in comparison with SPEED specialists. Further univariate analysis showed that SPEED specialists had a higher body weight, BMI and sum of SF corrected for body height than TECH specialists (Table 1).

<<<

 

[digger jr]

Hi Dave!

I always thought the bigger sliders. had an advantage, then you see Mikaela Shiffrin ( 5’7” tall 141lbs ) on the circuit killing it.

 

Edited March 24, 2023 by digger jr

[Aracan]

I cannot reproduce it, but in high school physics we did the calculation for two skiers, a lighter and a heavier one, to see which one would glide faster. Bottom line: Since friction does come into the equation (unlike Galileo's experiment), the heavier rider will glide faster, all else being equal.

[drschwartz]

So, having been a high school racing coach for 23 years, I don’t think the answer has much to do with the free fall discussions above. Here are my thoughts.

1. During a straight, gliding section of a race course, the heavier rider has the advantage. He/she will overcome the friction caused by wind resistance and snow much better.

2. However, in turns, the lighter, more agile rider clearly has an advantage. Since a race course is mostly turns, smaller riders tend to have an advantage. Can’t even count how many times a 12 year old has beaten me just because they can go straighter down the course.

3. Of course the largest determinant is how well the rider holds their edge and holds their line through the course. The more talented rider always wins.

Paul

[bucky]

The closest comparable I can think of in a controlled situation is Boy Scout Pinewood derby cars.  There are very strict rules on weight and the total weight of the car cannot exceed 5 ounces.  They race on a matched track from the same release point.  I can tell you that the margin of error on the scale is +/- .1 ounce and the 0.1 matters so you put on very small weight to get the actual weight to 5.04 ounces.  A car that weight even a fraction of an ounce more will have an advantage all other things being equal.  A difference of say 20% (4 oz v 5 oz) will make a big difference in results and the heavier weight can overcome difference in lubrication and aeodynamics.

So to me it can play a part of the equation.

Look at downhill racers - most are pretty large.  Makes less of a difference in technical events.  Would probably make more of difference in BX as compared GS or SL.

[JohnE]

The 130# person has 130# pulling him toward the center of the earth. The 230# person has 230# pulling him. 

The aerodynamic drag on the bigger rider is bigger but not 77% bigger. So the heavier rider has the advantage. 

[Jack M]

Fat is fast.  Yes, all else equal, the heavier person will be faster.  One reason is they have more momentum which overcomes friction, air drag, and momentary forces (bumps, ruts, etc).

[Neil Gendzwill]

The answer to this question as with all real-world physics is that it's complicated.

[drschwartz]

But again….

Heavy means momentum. Momentum makes changing direction much harder. Lighter, more agile racers have better performances in slalom, and even in GS courses. When you get to downhill courses, the equation changes.

Paul

[st_lupo]

I'm not sure it is the momentum that makes changing direction harder.  Removing the rider's skill from the equation and looking at the physics: the centrifugal force needed to change direction is linearly proportional with mass; and while I'm not sure, I would guess that edge hold is also a linearly proportional to mass.  So I think that from a purely mechanical sense, the potential for performance in the technical disciplines would in an ideal situation be independent of the system's mass.  (Or perhaps the increased rotational inertia of a heavier rider has a larger effect?)  However, given that the rider's ability and agility is a part of the equation in a race, lighter seems to correlate to body-agility, which then impacts the total biomechanical system and likely dominates technical disciplines in being quicker edge-to-edge?  (In speed disciplines I would assume that body mass will play an increasingly important roll and heavier = faster to an increasing degree).

[inkaholic]

3 hours ago, drschwartz said:

So, having been a high school racing coach for 23 years, I don’t think the answer has much to do with the free fall discussions above. Here are my thoughts.

1. During a straight, gliding section of a race course, the heavier rider has the advantage. He/she will overcome the friction caused by wind resistance and snow much better.

2. However, in turns, the lighter, more agile rider clearly has an advantage. Since a race course is mostly turns, smaller riders tend to have an advantage. Can’t even count how many times a 12 year old has beaten me just because they can go straighter down the course.

3. Of course the largest determinant is how well the rider holds their edge and holds their line through the course. The more talented rider always wins.

Paul

This 

When in the turns gravity is pulling the heavier rider down, off line and late, toward the next gate where the lighter rider can hold a straighter line.

I watched OddJob set a fastest time on a family fun course. They continued to allow timed runs for fun, not prize, and KarverKai, 9yrs old, learned each run getting tighter to the skier gates and chipped away at his time till he had the snowboard FTD thru all the days ruts later in the day. KK was about 80lbs to OddJobs 210?.

Also @Dave Winters We have seen many times now when Cody has been faster than the larger racers in PSL only to be beat because of a mistake by Cody. His time, especially in PSL, is coming real soon and this last race is the start of that (2nd qualifier and 4th final).

ink

[Jack M]

1 hour ago, drschwartz said:

But again….

Heavy means momentum. Momentum makes changing direction much harder. Lighter, more agile racers have better performances in slalom, and even in GS courses. When you get to downhill courses, the equation changes.

Paul

True, I was just thinking of friction and drag. 

I wonder though, if two racers had different weight but the same strength-to-weight ratio such that the heavier rider could deal with direction changes with as much agility as the other...

[ShortcutToMoncton]

2 hours ago, JohnE said:

The 130# person has 130# pulling him toward the center of the earth. The 230# person has 230# pulling him. 

The aerodynamic drag on the bigger rider is bigger but not 77% bigger. So the heavier rider has the advantage. 

But unless I misunderstand my physics 101, I don’t think “x pounds pulling him towards centre of the earth” makes any difference. Gravity pulls equally on both heavy and light objects. 

All else being equal, a piece of crumpled lead falling towards the centre of the earth will fall at the same rate as an identical piece of crumpled paper. 

Of course, in the real world, little else is equal. For an athlete more weight generally means more strength. Both momentum and friction are affected by mass. And wind resistance is affected by the size of the object.

But the point is that a rider’s weight does not strictly affect the pull of gravity towards the centre of the earth. 

[Spiny Norman]

Is this a Gravity vs Terminal Velocity vs Coefficent of Drag discussion?

 

Cuz if it is count me out! I am decent at crosswords however.

 

https://en.wikipedia.org/wiki/Terminal_velocity

 

https://en.wikipedia.org/wiki/Drag_coefficient

[ursle]

Hmm, a straight glide test will be won by the heaviest, most coordinated rider, yet a race course will be won by the rider with the best eyesight, balance and strongest core, that also gets the most rebound.

[John Gilmour]

Depends on the course . Any course with a longer flatter glide section at the bottom  where a racer is going fast will heavily favor the heavy racer who holds more momentum.  Any course with a long flat section in the middle will also favor the fat guy because even though the aerodynamic drag will be lower at lower speeds - it still figures in.
 

Icy conditions favor the heavy guy who has more downforce for cutting and melting the ice.

But in a course with packed powder where the snow can not support a Lot of lateral weight with constant pitch that is more than moderate and an extremely offset course without any flat sections the lighter more agile rider is favored .

 

As a slalom skateboarder course setter…I try not to set courses that favor a glide contest of larger wheels , and heavy riders. I also strive not to set a course that is impossible for the bottom 70% of the riders and also one where the most skilled fastest riders actually tend not to bunch up but even put more space between themselves and the average racers.  One where the fastest racers can keep going into each section hotter and hotter and come out on fire.  Where as in some sections the lesser racers have to be a little more conservative. 
 

 Course reading skills should be a larger part of winning than just riding a longer board with precise wax. I’d rather be impressed with someone’s skills than their gut and wax.

Edited March 25, 2023 by John Gilmour

[st_lupo]

9 hours ago, ShortcutToMoncton said:

But unless I misunderstand my physics 101, I don’t think “x pounds pulling him towards centre of the earth” makes any difference. Gravity pulls equally on both heavy and light objects. 

All else being equal, a piece of crumpled lead falling towards the centre of the earth will fall at the same rate as an identical piece of crumpled paper. 

Of course, in the real world, little else is equal. For an athlete more weight generally means more strength. Both momentum and friction are affected by mass. And wind resistance is affected by the size of the object.

But the point is that a rider’s weight does not strictly affect the pull of gravity towards the centre of the earth. 

All things being equal the crumpled paper will not fall to the center of the earth at the same rate as the crumpled lead of identical shape.  Gravity (as in 9.8 m/s^2 or 32.2 ft/s^2 for those that are measurement system challenged) is an _acceleration_ that effects all things on earth equally, and not a _force_.  The force of gravity would be F=mass__kg * 9.8, which is obviously greater on the lead (heavier) object and less on the paper (lighter) object.  Given that both objects in this thought experiment have an identical geometry, they both have the exact same drag at a given speed.  Since the lead ball has over 16x the mass of the paper the drag force is nearly negligible compared to the paper ball.  For example:

 

F_gravity_paper = 9.8 [m/s^2] * 1 [kg] = 9.8[N]  

F_gravity_lead = 9.8 * 16 = 156.8 [N]

velocity_paper = velocity_lead (at our initial conditions)

F_drag_paper = 3 [N]  (just pick a number, at some speed it will have this much drag)

F_drag_lead = 3 [N] (same geometry and speed as the paper ball)

F_resultant_paper = F_gravity_paper - F_drag_paper = 9.8 - 3 = 6.8 N (working to accelerate the paper downwards)

F_resultant_lead = F_gravity_lead - F_drag_lead = 156.8 - 3 = 153.6 N (working to accelerate the lead downwards)

F_resultant_paper = mass_paper * acceleration_resultant_paper 

----> acceleration_resultant_paper = F_resultant_paper / mass_paper = 6.8 / 1 = 6.8 [m/s^2]

F_resultant_lead = mass_lead * acceleration_resultant_lead

----> acceleration_resultant_lead = F_resultant_lead / mass_leas = 153.6 / 16 = 9.6 [m/s^2]

And, all things being equal, the lead ball will in fact have the higher terminal velocity because the drag at terminal velocity for both balls needs to counteract their gravitational "force" (which is 16x larger for the heavier lead ball).  Since drag increases with the square of the velocity, this means the lead ball will have a terminal velocity that is 4x larger than the paper ball.

9 hours ago, Spiny Norman said:

Is this a Gravity vs Terminal Velocity vs Coefficent of Drag discussion?

 

Cuz if it is count me out! I am decent at crosswords however.

 

https://en.wikipedia.org/wiki/Terminal_velocity

 

https://en.wikipedia.org/wiki/Drag_coefficient

From a purely mechanical sense (minus the rider's capability), yes it is!  But the basic idea is very simple.

46 minutes ago, John Gilmour said:

Depends on the course . Any course with a longer flatter glide section at the bottom  where a racer is going fast will heavily favor the heavy racer who holds more momentum.  Any course with a long flat section in the middle will also favor the fat guy because even though the aerodynamic drag will be lower at lower speeds - it still figures in.
 

Icy conditions favor the heavy guy who has more downforce for cutting and melting the ice.

But in a course with packed powder where the snow can not support a Lot of lateral weight with constant pitch that is more than moderate and an extremely offset course without any flat sections the lighter more agile rider is favored .

 

As a slalom skateboarder course setter…I try not to set courses that favor a glide contest of larger wheels , and heavy riders. I also strive not to set a course that is impossible for the bottom 70% of the riders and also one where the most skilled fastest riders actually tend not to bunch up but even put more space between themselves and the average racers.  One where the fastest racers can keep going into each section hotter and hotter and come out on fire.  Where as in some sections the lesser racers have to be a little more conservative. 
 

 Course reading skills should be a larger part of winning than just riding a longer board with precise wax. I’d rather be impressed with someone’s skills than their gut and wax.

This!  This is what separates good courses from bad courses and makes things exciting!  However, I'm not completely convinced (again in the purely mechanical sense) that performance on ice should favor either the heavier or the lighter system.  The edge hold needs to resist the centripetal force of the turn, (m * v^2) / r.  I don't know exactly how the edge-hold force would be described but I'm pretty sure that for "idealized" edge hold on ice (the gouge through the ice doesn't buckle) that it is roughly linear with the rider's mass (something akin to force due to friction), ie f_edge = mass*ideal_ice_hold coefficient.  In this idealized case the the turn radius winds up being independent of the system mass (and edge length for that matter) and

radius_min = (v^2) / ideal_ice_hold

I'm guessing that when riding "on the edge", ice and packed powder act in a very different and non-linear fashion (buckling. etc), and in such a case,  the system weight, edge length, etc suddenly plays a much larger role. 

[ShortcutToMoncton]

You’re quite right of course, the objects will accelerate the same, but the heavier object should have a higher terminal velocity. Thanks for taking me back to high school physics, this is great!!  

I was thinking that approaching t. velocity would not be applicable in a race course scenario, but of course it definitely could depend on real world course sections and the conditions (snow, wind, etc).

[st_lupo]

It doesn't just effect terminal velocity but acceleration as well