Rather than clutter the jump calculator page more than it is already, this is a somewhat streamlined version that will hopefully answer some questions I tend to get via email.

* “Do I really need to do all the math and follow these suggestions?” *Besides the fact that I did some of it, and you can check it for yourself (to make sure I didn’t screw it up), that is up to you, but in short, no, you’re a free agent. You can play with the transition (or curve), the takeoff lengths of the equilibrium flat segment to change the height, and the landing, all of which will impact the soil budget, feel, and flight line, but the steps below will get you something better than most people with shovels and a prayer build…not that winging it or eyeballing it is a bad thing, but it is possibly more dangerous or less predictable (especially if the jumps or landings happen to be way off the mark). The information below will help you get closer to the marks made by engineers, physicists, and geeks like me that have spent time thinking about these things, but do as you want or wish while moving away from those marks.

If you’ve spent any time looking closely at the plethora of jumps on the web it is easy to conclude that there are a myriad of jump and landing shape flavors that seem to work and (maybe) feel just fine. People even jump things that were not intended as a jump at all, but they always have three things in common: a certain speed and angle, and the inescapable Laws of physics that are impartial and have no cares about silly notions of being a free agent because in reality you are not, you are a prisoner to those boundaries. However, understanding the boundaries will go a long way to making sense of it all and leaves you “free” to determine where you want to push the boundaries to get through this life. Ignorance might be bliss, but in my mind knowledge and knowing the questions or gaps that we are ignorant of is enlightenment, and a much more fulfilling or blissful life.

I will end with the obvious fact that jumps can be very dangerous, they can end lives or change them forever. Being confined to a wheelchair and possibly needing a ventilator because nerves from the neck to the lungs were severed is no way to live. Some of the jumps you see in videos and stills, and the things that you might make with the knowledge on this website could possibly kill or maim someone. Think before you send it or build it “too” big. It doesn’t take much more than falling from your own height to kill you, and less if adding extra speed into the equation. I like endorphins, but for me some things are not worth the risks. Know your boundaries, read up on EFH, and seriously consider the damage you could do to yourself and others.

- Get familiar with information and images on the jump calculator page
- Jumping is dangerous, and may cause serious injury or death (see this).
- Build and jump at your own risk, no guarantees are promised by the numbers output by the ramp calculator or spreadsheet, or how you might build the ramp yourself, but hopefully this page can get you in the ball park (if you know what average launch speeds will be– don’t forget speeds will slow as you climb up ramp, and drag friction will reduce the Range, sometimes significantly if windy, leaving you short).
- Speeds can be increased beyond what is measured if transitions are pumped, see this.
- The calculator ASSUMES same launch and landing height, i.e. that they are level.

- The ”jump angle” or θ = the angle of the bike the instant the back tire leaves the ramp, which should be very close to the wheel base angle when the front tire is at the lip. The bike jump calculator is for a “point” of mass. In turn, R will have to be shortened by: (wheelbase in feet or meters) x sin(jump angle) = distance to shorten R. For example, perhaps err for extra large 29er wheelbases that are somewhere around 46 inches: 46in/12in/ft= 3.83 ft, meaning 3.83 feet x sin(jump angle) = distance to shorten R for XL 29ers with 46 inch wheelbases.
- Read and understand this information about lips and transitions to the lip.
- Read all of the above again.

- Launch and landing speeds will be the same (or negligibly different) if the launch and landing heights are the same.
- For a slower/softer landing, landing ramps can be elevated (a step-up), but this will change the range, R, to a shorter distance.
- If landing at a lower height than takeoff then R, or the the landing lip, can be pushed farther from the takeoff lip. Please see the “safer jump” pdf documents linked at the bottom of this page for details about the best landing ramp design.
- WIND and rider behaviors like pumping, lifting, braking, spinning, flipping etc. could change any of the variables (h, R, t, and the angle of launch)– in other words the parabolic line of flight as as predicted by the calculator will be altered, altering R.
- Wind and drag may become a factor if strong enough or H and/or R is great enough.
- The calculator is for RIGID forks AND RIGID tails, i.e. hard-tails. Suspension can change the angle of launch, thus H and R. Recoil may also affect the outcome.
- Test your creation and measure carefully. How fast were you going, what exactly is the lip angle, and did you pull up or pump? Was it windy? What tire pressure and how knobby? Adjust your creation accordingly, perhaps with a correction coefficient
- Use a level or other means to check angles.

#### Step-By-Step Jump Build Guide

**The Ramp**

- Read and understand 1-11 above
- Use the Scientific Method: “The standard starting point for a non-inductive analysis of the logic of confirmation is known as the Hypothetico-Deductive (H-D) method. In its simplest form, the idea is that a theory, or more specifically a sentence of that theory which expresses some hypothesis, is confirmed by its true consequences.” source
- By “non-inductive” they mean empirical data. We ain’t gonna wing here. Measure shit… including the consequences.
- “…when researchers take an inductive approach, they start with a set of observations and then they move from those particular experiences to a more general set of propositions about those experiences. In other words, they move from data to theory, or from the specific to the general.” source
- we intend to move from “we are going about x mph because we actually measured it a bunch,” to “we want to move this much dirt or want to go this far and/or high (considering effective or equivalent fall heights as well)

- Ask a question: How far or high do I or can I (based on my speed) jump?
- Gather empirical data (observe and measure it): How fast is the low, average, and high speed at the bottom of the jump (and at the lip)?
- Form a hypothesis: Math abc says I should go this far and high, I think jumpers will go xyz.
- Experiment by measuring speeds and jumping to see if the math and hypothesis are true.
- Review and scrutinize the data…Did I make it past the knuckle, by how far?
- Was the conclusion true or false, by how much, is a new hypothesis needed to explain the mismatch of prediction and reality? Why did what happen?
- Adjust and test it again until it is “dialed” in.
- 3-6 is the main method, and often goes back to 3 to start again to dial it in better.
**SPEED**at the ramp bottom: Mark the location where the transition up to the lip will begin with a pin flag or stake or rock that won’t harm anyone while getting the speed measurements.- How fast are you going at the time you hit that mark? You probably have to measure before you hit that mark…usually 10 feet or more depending on speeds or how good your stopwatch accuracy is, if too fast increase the distance
- Measure how fast you will be traveling at the jump site location…where the transition up will begin. How? Distance = Rate x Time or Rate = Distance/Time
- Use a tape measure and stop watch, the Speedclock app, or some other means. They sell radar guns too, but some may not be accurate at low speeds.
- Did one of your science teachers explain Accuracy, Precision, and Significant Figures? If not read this.
- If your radar gun doesn’t have at least one significant digit after the decimal point…10.0 or 10.00 vs 10, go for the one with two decimal points, it should be more accurate.
- The above does not mean one measurement, this is science yo, data will be an average. How much, or how many runs? That is up to you, but more is better, and will give you a good idea of low and high speeds for dialing in the landing knuckle and ramp length as well. More than 10 runs would be nice (and hopefully fun). Make a data table or something with your measurements.
- If speeds vary by more than 5 mph you may want to consider speed checking people to control speeds. Coasting in rather than pedaling should be goal as pedaling can significantly change speeds. Pedaling on a jump trail is sort of a cardinal sin btw. It’s kooky. Modify the design for gravity, not burning extra calories that could be used for more runs.

**RAMP HEIGHT**: you’ll need this for the next step below, the speed at the lip, but we are jumping ahead a little bitat the ramp lip: Now you know your speed…at the bottom, NOT the lip. You will be going slower at the lip because it will be higher than bottom of the lip where you measured. This is a conservation of energy problem.**SPEED**- vf^2 = v0’^+2*2gh Vf is the final velocity at the lip, V0 is at the bottom where you measured. In a program like Excel it looks like this: vf =SQRT((v0^2+(232.1767*ramp height))*1/2.151) answer will be in mph at lip
- This is a deductive method, you could measure speeds again at the lip, but if you are already started testing the jump and are making it past the knuckle why are you reading this? If you are hitting the flats, or run-out there are several possibilities as to why.
- Lower Range and Lower Height than 45< 45 degree lip < Lower Range and Higher Height than 45
- Now you know your *approximate* lip speed

- You could skip 3 and 4 and just start building your damn ramp too, but knowing the speed, not some assumption about how fast you “might” be going, is better, whether the ramp comes first or is already there and you need to tweak it because someone didn’t do science they winged it, or boosted it. Moving pencils on paper is easier and faster than moving dirt, but test riding with no math might be more fun..
**TAKEOFF**: Takeoffs should incorporates a 0.25-0.30 second takeoff equilibration or equilibrium segment…according to the “industry” standard used by some ski jump engineers so users hit the lip smooth like and don’t get bucked…unless of course you want extra pop that could put you upside down on your cervical spine…which could still happen with equilibration, but it’s not as likely.- Use your speed/s for this: =(vf*0.25*5280)/3600= # of feet of your flat spot segment should be for 0.25 seconds of equilibration from lip to where the transition starts/stops.
- For example, 14 mph at the lip means a 5.13 ft flat spot from the lip down to the transition’s end at whatever angle it will become.

**TRANSITION**: Transitions that keeps g’s below about 1.5 are better for rider stability. (How do I know this? Again, I read some of the ski industry standards, or people trying to make jumps safer, see the PDFs below).- The best we (or I can do) at this time is to use the speed at the bottom of the transition (V0), and the assumption that a circular tranny is being used though a clothoid is better (more on that at a latter date). For now we will err on the side of a circular radius for the tranny because they will be more likely to cause bucking than a clothoid, however we are using a “flat” takeoff.
- Centripetal acceleration on tranny: v0^2/r min= gy or r min= v0^2/yg (g = gravitational acceleration, y=allowable centripetal acceleration in units of g…gs (1.5 gs “best”, 3 gs max, but not recommended),
**r min**, ft = v0^2(1609.3*5280)/(14.7*3600*3600) (this is the approximate transition radius minimum, but the next step (15) is a better approximation of what to shoot for.)

- Now that we know the flat takeoff length and the tranny radius (r min), we can estimate the length of the tranny if clothoid.
- Lc (length of clothoid segment, two segments total make the clothoid), Lc= A * sqrt of slope to lip angle, A= sqrt r min ^2 *slope to lip angle so Lc= sqrt r min ^2 *slope to lip angle * sqrt of slope to lip angle x2:
**~Total ramp length min**(if clothoidal), ft = SQRT((RADIANS(r min^2)(lip degrees))SQRT(RADIANS(lip degrees)))*2- This means the tranny length to the flat takeoff = ~Total ramp length – flat takeoff length
- So at minimum give the transition to the flat take off this length, and make a smooth transition to the flat takeoff using your artist/sculptor eye.

- Back to the approximate
**HEIGHT**: There are a myriad of possible heights, but:- If the ramp is entirely circular all the way to the lip: This is not recommended as it can cause bucking or put riders upside down onto their heads depending on their speed and the radius. Anyway, it can give us a minimum height so you can think about soil volume or wood needs. ~ ramp height if circular = (lip degrees*r minimum)/90
- The ramp is a cycloid, clothoid, or some other shape top to bottom, or that plus a flat takeoff
- This is the best I can do for now for ramp height:
- We know the takeoff length and degrees, so we can get that part of the height: SOH…Opposite or the
**height of takeoff**= sin of takeoff angle*takeoff length (in Excel: SIN(RADIANS(takeoff angle))*takeoff length). The takeoff run is found using the Pythagorean theorem: takeoff run = sqrt(takeoff length^2-takeoff height^2) - The height of the tranny is a little more complicated, and since I’m not going down the clothoid rabbit hole yet this is the best I can do: We know the total length and the takeoff length, so the tranny length or hypotenuse = total length – takeoff length. The tranny rise is a stretch, more later, but for now this is close:
**tranny height**or opposite side = sin of takeoff angle*tranny length - The
**total height**approximately = takeoff height + tranny height

- We know the takeoff length and degrees, so we can get that part of the height: SOH…Opposite or the

- 1-16 is the ramp or jump, good luck (Read and understand 1-11 at he top of this page)

#### The Landing

- Ask a question: How far or high do I or can I (based on my speed) jump?
- Gather empirical data (observe and measure it): How far does the jump send riders, average, low and high ranges (distances from the lip)?
- Form a hypothesis: Math abc says I should go this far and high, I think jumpers will go xyz.
- Experiment by measuring jumping distances to see if the math and hypothesis are true.
- Review and scrutinize the data…Did I make it past the knuckle, by how far?
- Was the conclusion true or false, by how much, is a new hypothesis needed to explain the mismatch of prediction and reality? Why did what happen?
- Adjust and test it again. Until it is “dialed” in.
- 3-6 is the main method, and often goes back to 3 to start again to dial it in better.
**Mark**the location where the landings occur.- The jump range from lip to knuckle (at the same height),
**Range**, ft = s= vf^2sin(2θ)/g θ= flat takeoff lip degrees, s= ((vf*0.44704)^2(SIN(RADIANS(2*θ))/(9.807)))3.281 - This will give you the approximate distance from lip to knuckle.
- The landing ramp should have an angle similar to the take off.
- How long should it be after the knuckle? What was the range of speeds, consider the slow speed as the knuckle, and the fast speed as the “end” BUT we need to account for rider input and give another 2-3 bike lengths before transitioning to the flats or run-out as well
- Riders can shorten their range by squashing it, by lets say 5 mph. It is up to you if you want to shorten the knuckle by this…take your slow speed and subtract another 5 mph for a new range.
- Riders can boost by about 3 mph on a flat lip (more if curved, but we are not concerned with that in these examples)…take your fast speed and add another 3 mph for new range. Give another 2-3 bike lengths before transitioning to the flats or run-out
- Try to incorporate a safe equivalent fall height (see below)

- 1-14 and the EFH info below is the landing ramp, good luck (Read and understand 1-11 at he top of this page)

**Equivalent Fall Height**

The table and landing ramp should be designed to lower the impact upon landing to a “safe” distance. The goal is to create a landing where the impact is nearly the same or does not surpass the EFH along the entire landing. This is usually involves a landing that gets steeper as it gets farther from the knuckle. EFH is typically around a 4 feet high maximum in the ski industry. Meaning when someone lands they are effectively landing with an equivalent impact to the designed EFH, whatever that might be (usually under 4 ft). What that should be for bikes I am not sure. It could be higher with suspension, but I can’t say by how much. The safe bet IMO is to stick with the research sited in the PDFs below. EFH considers the kinetic energy of the landing velocity perpendicular the surface divided by *mg*, EFH = velocity/mg, thus steep farther away where velocities increase. The landing mimics the parabolic flight path to some degree.

- Ramp/Jump Physics (applied math) PDFs:
- Safer-jumps that-limit-equivalent- fall-height
- A design rationale for safer terrain park jumps that limit equivalent fall height
- SAFER-JUMPS-DESIGN-OF LANDING-SURFACES-AND-IN-RUN-TRANSITIONS
- Jump-Landing-Design-Limits-Normal-Impact-Velocity
- Ski jumps are not necessarily bike jumps, but for flips and such it may be best to go with these standards though the landing ramp may be a different setup: International Ski Federation (FIS) Freestyle Committee Aerial Site Specifications (note the continuous curved transition)

- other info: here, and here
- also see this:

- Contact me about consulting
- A downloadable spreadsheet is forthcoming