Most of this page is dedicated to pump track rollers, but it should certainly help inform the application of these principles to “whoopee” like drains and rollers on or on the side of trails. More on grades and grade reversals is here.
The Brachistochrone could be the best curve or cycloid for dirt jumping to keep things fast, and the companion curve of the cycloid could make for a really good/efficient roller, especially on dirt pump tracks where friction loss is greater than a cement or asphalt track. However…
Fast is one thing, smooth is another. Or fast is smooth, smooth is fast, so consider clothoids (see Bike Jump Design page). A cycloid or tautochrone could work for berms, but it depends on where riders come down the entry and out the exit (they are probably going to follow a clothoid path along whatever is built). Of course laying this type of berm out in the field would be a little tedious, if not futile. Also, is it really necessary, even on a pump track? And wouldn’t it suck to have cookie cutter replicas at nearly every berm, or roller for that matter? Would the character and art be lost? Yes. These curves/shapes are probably the most important on pump tracks where the goal is easy pumping and conserving as much energy as possible rather than losing it. Nonetheless, knowing what this means and how it works can help builders understand the basic shapes and how to get more (or less) speed when needed, and how to not stray too far from efficient form, flow, and motion.
I did test Brachistochrone rollers (see below). Long story short, don’t try this at home.
A bit too peaky
Looks are and aren’t deceiving, tests certainly confirm hypotheses on a certain look. Short answer: more rounded is better. The companion curve was too peaky, oh well, I tried. See images of Brachistochrone curves above and below. I think if this shape was 4-5 ft tall maybe it would work, or maybe not. It might be fun to test. Testing these companion curve rollers was not that fun, or it was more disappointing than fun. I had to try…and now you don’t have to hassle with it unless you want to try it yourself. Maybe you can try the 4-5 high ones, but that’s a lot of wood for the template, and dirt to move.
A solution could be to combine the top of the Brachistochrone with the bottom of the companion curve, but ultimately pedal strike avoidance and flow is key. Something like a sine wave (explained below). It comes down to art and feel, but also the conservation of energy which cannot be ignored, which should be understood and exploited. Not only is less peaky more flowy at higher speeds, it is also easier to manual. However, less peaky and lower means a little less fast. At this time I’m not sure if softer and more flowy rollers can make up for the potential speed loss.
Pedal Strikes on Rollers
A better solution, or something to consider (especially if you are designing for stider bikes), is a roller that considers pedal strikes or strider bikes getting stuck, and the critical flat to arc transitions:
Making A Sine Wave Roller (10:1)
The equation for a 12 inch tall sine wave roller at Lee Lee McCormack’s recommended 10:1 ratio…(10 ft to 1 ft, 120 in to 12 in) y = 6sin(1/19.0985 x) Try it here:
I printed 1/4 of the 10 ft template on 3 pages, cut them out, taped them together, then traced it and flipped it 4x to complete the frame/guide, but at only 8 ft long one end gets cut off by 2 feet, but it’s fine for shaping rollers as the wood guide can be rotated. Having another one that is cut in half at 5 feet is nice for doubles or other features. A level will help make them even. Pedal strikes are not a concern with this sine wave option. Taller rollers will need another equation…more on this to follow.