This is a recap of part of the jump design page to drive home the force of gravity.
Transition G Forces
If they are circular…
^As you can see tighter transitions and higher speeds don’t mix well.
Circles are not ideal transitions for jumps. The clothoid (or Cornu or Euler’s Spiral) is best, so is a flat/linear take off with about 0.25 seconds of time x the take off speed, typically a flat/ish segment with little to no curve. So at 15 mph (6.7 m/s) x0.25 seconds the flat spot will be 1.6 m or 5.2 ft. This means higher and longer jumps, even for small ones, or jumps with low angles (sub 30 degrees). The clothoid shape minimizes jerk or buck stress on riders from the curvature of the ramp, and their speed. Gravity slows them down as they climb to the lip, and they can simultaneously speed up relative to the curve, especially on a sharper radius or curve as they increase or preserve angular momentum. A clothoid radius is not constant, but variable along its length, the curvature at any point along the clothoid is equal to its arc length (measured from the origin). See the landing pdfs below for more information. Also see the spiral turn videos on the turn design page for spiral clothoid-like arcs. The arc of a clothoid lip is somewhat similar.
Bigger circular transitions are less jerky, a clothoid even less so. The time spent on a clothoid to the lip is nearly double that of an equivalent circular arc, thus its a smoother tranny. The minimum radius should be related to the speeds typically experienced going up the lip to limit the Gs to 1.5gs, and about 3gs max on the landings or riders will feel jerky transitions and hard landings, not flowy ones. (r min = v^2/1.5*g or v^2/14.7m/s^2). This translates to keeping jump speeds below 16 mph with a 12 ft radius…might as well go for the softer bigger tranny. However, this number should be used to determine the correct clothoid shape. The minimum r should be multiplied by total angle that the rider will rotate in the transition from the slope of the entry to the angle of the takeoff lip. The transition length should typically be close to double what the minimum circular distance would be, which is the r min x degree change from bottom to lip x2 (r min x the downhill slope angle + lip angle).
At this time I do not know the g forces for clothoids, but a safe bet might be to consider that the time spent on a clothoid to the lip is nearly double that of an equivalent circular arc. In theory the G’s in the graph above could be nearly halved for the speeds.
For tricks, such as flips and such, a curved radius is preferable, but the amount of that curve is a little complicated and related to the speed and pumping body mechanics of the rider ascending to the lip at a given speed and number of gs from the combination of speed and curvature. Tricks can still happen off of a ramp with a nearly linear takeoff that incorporates the 0.25 second takeoff equilibration into account, but flips will be harder to accomplish.
Why do Curved Transitions to the Lip Allow Boost?
- Pumping lowers the moment of inertia (~rotational difficulty), or increases speed by reducing the the radius of the jump arc (r). I=mr^2
- By reducing Inertia by making r smaller pumping effectively increases speeds or rotation on the curve, the speed you think you know at the lip may actually be FASTER than what you might measure to calculate the jump range or height because pumping adds or boosts energy into the event.
- Boosting vs. Squashing or “racering” Jump Energy
- Boosting: riders bend at the bottom, then extend at the top (and usually the reverse on way down). They move their center of mass to the rotation axis, reducing I and increasing v, as well as the parabolic flight trajectory (at most around +/- 15%?, probably less unless really skilled…at any rate, that can change jump distances and heights…meaning a 10 foot Range may need at least another 1.5 feet and then some if the rider changes the takeoff angle, which is quite likely when boosting or “popping” off lips, especially on booters with fast approaches and tighter radii.)
- Racering or Squashing: riders suck up or effectively flatten the transition curve or r, as well as the parabolic flight trajectory, and speeds may actually be lower than measured at the lip
- Speed is a function of knee bend pump, which is enhanced or squashed down energy, that changes the r of curved transitions, much less on plane ones where riders can jump off the lip, but can’t really boost it or punch it up still higher by lowering inertia
- Also worth noting, and more than I can comment on in detail at this juncture, is that suspension can modify jump estimates. I can’t say how much at this time other than the fact that plane take offs or larger radius transitions will be more predictable. Riders might be able to get more pop or boost if the ramp is short enough as they can use shock rebound to get more pop if they and/or the ramp itself compresses (or “preloads”) the shocks then releases them at the lip.
- Something else to consider is that if riders pull up, rather than let the bike’s ghost riding parabolic trajectory float below them, they are changing the launch angle as well.
- Soft transitions or clothoids, nearly linear takeoffs that consider the 0.25 second takeoff equilibrium, and minimum radius to lower gs below 1.5 will go a long way to “better” jumps.