# Skimming over obstacles

Maybe you’ve heard that the faster you ride through rock gardens, the less you drop down between the rocks, and the faster and easier you can ride. That idea makes some sense, but the question is: How fast do you have to go?

I wish I’d gone farther in math. If I made a mistake, I’m sure you’ll let me know!

 Wiley skims at Left Hand Canyon OHV Area.

Imagine a gap three feet wide and 26 inches deep. Ignore suspension, tire flex, body English and every other variable.

When a wheel rolls off the first edge, it begins to drop. The slower you’re riding, the longer it takes to get across the gap, and the farther it drops. For example, at a snail-like 8 mph, the wheel drops almost 13 inches — and POW! — it hits the next edge dead-on. That, my friends is a dead stop.

The faster you go, the less the wheel drops. Twice as fast equals one-quarter the drop. At 8 mph you drop a stop-dead 12.6 inches; at 16 mph you drop a pond-skimming 3.2 inches.

At around 15 mph your wheel drops just less than four inches, and a cool thing happens. Four inches corresponds to a 45-degree angle from your hub. At this angle, the impact is half upward and half backward. Above this point, the impact pushes the wheel mostly backward (it mostly slows you down). Below this point, the impact pushes the wheel mostly upward (it bounces you into the air). From what I gather, this four-inch point is the threshold between getting stuck between the rocks and skimming across them.

This “four-inch speed” is directly related to the gap distance. Simplified:

 Gap Threshold speed 1′ 5 mph 2′ 10 mph 3′ 15 mph 4′ 20 mph 5′ 25 mph

As you go faster than this threshold speed, the tendency to skim becomes even greater.

### Better hang on

That is super cool, but there’s a catch. Kinetic energy increases with the square of velocity. Twice as fast equals four times as much kinetic energy. Four times the jolt. Four times the WHOA! Racers like Peaty and McCormack stay high in the rocks, but they also contend with serious forces. One more reason to be strong!

### So what does this all mean?

1. Try to ride through rocks above the “four-inch threshold” speed.

2. Faster is better, as long as your bike and body can handle the forces. That’s why race bikes have to be so stiff, and racers have to be so strong.

Right on. Go forth and skim!

### Real-life application

The Pit of Despair in Moab is pretty scary. It’s about five feet wide, with a threshold speed of about 25 mph (pretty fast!). That explains why Sacha made it easily when he pinned it, and why he got balled up when he rolled it slowly. Next year, I’ll rock it in second gear. BRAAAP!

 Sacha makes it on my bike. Sacha didn’t quite make it on Diane’s bike.
19 replies
1. Jonas says:

Lee, I admire your scientific way to make things understandable. However, you make some mistakes or big simplifications so that not everything is right from an scientific point of view. If you hit a rock, no matter at what angle, there will always be a force upwards and one backwards. If you think about a total rigid system these forces will even be infinite!
The principle of linear momentum would be a better approach for this problem. If i will find the time somewhen I’d like to explain some things using everything I learned as an engineer.
However, in the end you’re right, you should go as fast as you can over rocks.

2. leelikesbikes says:

Good call, Jonas. I added a clarification. This was tricky to boil down!

3. Jason says:

Ouch! My brain hurts, I just wanna ride.

4. Josh says:

Obviously, we can then add the real world application that while the force is significantly greater at 20mph it is more vertical. Not only does this allow the suspension to work better (the force vector’s get close to the head angle after all) but your body is made to absorb vertical shock. Your arms, legs, spine, everything is made for vertical shock. That would be why 20mph doesn’t actually feel exponentially rougher.

Awesome how you overanalyze so much when it all translates to one thing… BRAAAP!

5. leelikesbikes says:

Well said.

Understand it, trust it, release it then BRAAAP!!!

6. leelikesbikes says:

Totally! You can bench press way more than you can military press. Do more regular pushups than headstand pushups …

7. Norcal says:

That is some good stuff… I love the geek in you..

8. leelikesbikes says:

>> Will MacDonald wrote:
>> Re: Skimming over obstacles…
>>
>> Dear Mr. Patron Saint of Pumptracks,
>>
>> Its so cool that you actually apply math to biking. It was also way
>> cool
>> meeting you in Moab with (I was the guy with Lianna, in case you
>> remember).
>>
>> However, one’s kinetic energy isn’t completely lost when he hits a rock
>> (except in the low speed case :D). Thus the ‘jolt’ (which is almost
>> directly
>> related to the CHANGE in kinetic energy) the rider feels does not quite
>> increase with the square of speed. This is because the impact becomes
>> more of
>> a ‘glancing blow’ as speed increases because the angles (associated with
>> changing direction) get smaller.
>>
>> That article got me thinking…What might be more important is how one
>> looses
>> a lot of momentum when one’s tires hit the far edge of the gap. For
>> instance,
>> at 15mph over a 3ft gap, you are in the air for 3ft/20mph=0.1seconds.
>> Multiplying this time by the accelleration from gravity means that you
>> are
>> falling at 2.25mph at the instant you hit the edge. As a result, you
>> will
>> lose 2.25mph of forward momentum if the impact arrests your vertical
>> motion
>> (because of the 1-1 ratio of rearward/vertical force with the 45deg
>> angle).
>> So, you have just lost 15% of your speed from a single impact and will
>> have
>> just under 13 mph to carry you across the next gap (not good!).
>>
>> If you are going faster, the time in the air (and vertical momentum) is
>> less
>> and so is the rearward/vertical force ratio. Basically you loose a lot
>> less
>> forward momentum.
>>
>> Of course you can jump before the gap and not loose any speed at all.
>> The
>> geometry of your parabolic trajectory means that you have to jump
>> one-fourth
>> of the height that you would fall, so 3.6″/4 or 0.9″ in this case. The
>> only
>> catch is that you have to time it correctly to within a fraction of the
>> 0.1seconds it takes to cross the gap. Speaking of rhythm, didn’t you
>> say
>> something about parts of Weir’s pump track feeling like a DH rock
>> garden?
>>
>> Awesome website, book, etc. Yeah, in case you hadn’t figured it out,
>> I’m kind
>> of a math geek. If you keep your articles open to this review stuff,
>> you may
>> have to change your website name to “Journal of Mountain Biking Science”
>> or
>> something. 🙂
>>
>> Cheers,
>> Will

9. scott says:

I’ve been waiting for this one!!!! Great stuff! Whether you wish to express the loss of forward speed as loss of forward momentum or as function of the angle of impact of the front wheel and the obstacle (whick will result in a new force vector being applied to the bike and rider), the results are basicall the same. There is an impact angle at which the summation of the vector will be back and down, and this will kill your speed, momentum, teeth,etc. If you can reduce the angle of impact, some of the vector will drive you UP, although much of the vector still drives you to the rear.
In a fully suspended bike this probably would have a lot to do with the fork and head tube angles, as well as with the instantaneous centerof gravity of the whole bike (i.e. is the bike being accelerated up or down just prior to the frontal impact).
“You can bench press way more than you can military press” What!?!? WRONG!!!! You can but for the wrong reason. try standing and seeing how much you can press outward using cables or bands, and then compare that to your military press numbers. You can bench press more because it is a completely artificial non-functional exercise in which your upper body is full supported. Bench press teaches you to lift heavy objects while you’re well supported flat on you back. Watch gymnasts work-out, not a huge difference between the numbers of hand-stand push-ups and regular push-ups they do, and not a bench press in sight.
Also there is a difference between the elastic shock absoption capabilities of the body and the ability to resist high g-loads. Astronauts go into space on their backs facing upward, not standing on their feet (to absorb the vertical stress) The upper body can be trained to absorb stress quite well Plyo-pushups, Medicine ball catch and toss, just as the lower body/legs/back can (box jumps plyo jumps)
Has Bobby called you out on this one yet??
Thanks for a very interesting article, Scott

10. leelikesbikes says:

Right on Doctor!

11. Josh says:

I was speaking more about the skeletal system than the muscular system. I just meant that you have more range of motion to deal with a vertical impact than a horizontal one while riding a bike. Therefore it is less jarring.

12. Pakster says:

Qualitatively OK but the math and physics are lacking. The wheel does not free fall. The bike falls but the rear is suspended by the back tire. The bike rotates on its center of mass, the net effect is to slow down the rate of fall. It’s too simplistic to argue about the angle of impact with the wheel tangent (it seems you are assuming the center of mass of the bike is on the wheel’s rim, otherwise some of the stopping force is just a torque about the center of mass, also known as an endo!)
Anyway, best to leave this to experimental science – go ride.

13. leelikesbikes says:

No wonder none of the companies I know have models for this stuff. They design the best they can, test key factors in house, then test ride. It all comes down to feel.

But this seems clear:

1. The faster you go, the higher you stay on the rocks and the more speed you carry.

2. The faster you go, the harder you hit things.

3. If you decide to go fast, make sure your bike, body and technique are up to the task.

Bracing for the next post …

14. Mike Johnstone says:

Well explained Lee.

The one point missing in this discussion though is the fact that the bikes momentum is separate from the riders. The more the bike falls into the crack the more the wheel becomes trapped as well explained above, and the more the direction of force will be back instead of up. This causes the bike to slow down. Your bodies mass however will not slow down unless you brace yourself against your bike, so when the bike slows suddenly you have to brace yourself in order to stay centered and balanced. This bracing is the harsh jarring you feel. And why we brace ourselves when braking hard.

The faster you go the more vertical the direction of force will be on impact and the easier it will be to stay balanced above your bike. Suspension and Head angle do have an affect on this as the easier it is for the wheel to come and over the obstacle the less the bike will be affected and thus the rider balancing above the bike.

15. leelikesbikes says:

Right on Mike.

That’s what I meant by “Ignore suspension, tire flex, body English and every other variable.”

There’s so much going on here … I friggin LOVE IT!!!

16. Jerry Hazard says:

I agree in basic principle and application, but…

I wonder about the statement “20mph has the 4x the impact of 10mph”.
This may be true for 20mph hitting in the same place as you would going 10mph, but at 20 the wheel is hitting higher up on the opposite ledge, therefore, the impact would be different, so the equation should change a bit, right?

Either way, thanks for posting this – and I woudn’t argue the basic idea that faster through the rocks is, well, fast through the rocks 🙂

17. leelikesbikes says:

Jerry, I think you’re right that the angle of incidence affects the impact force. That goes beyond my depth, but I know who to ask about this. Stay tuned.