{"id":2132,"date":"2025-12-15T11:02:43","date_gmt":"2025-12-15T16:02:43","guid":{"rendered":"https:\/\/students.bowdoin.edu\/bowdoin-science-journal\/?p=2132"},"modified":"2025-12-15T11:02:43","modified_gmt":"2025-12-15T16:02:43","slug":"pumping-without-pedaling-how-corners-turn-timing-into-speed","status":"publish","type":"post","link":"https:\/\/students.bowdoin.edu\/bowdoin-science-journal\/science\/pumping-without-pedaling-how-corners-turn-timing-into-speed\/","title":{"rendered":"Pumping Without Pedaling: How Corners Turn Timing into Speed"},"content":{"rendered":"

Watch a skilled rider enter a berm: they arrive tall, compress as the turn loads up, and rise on exit – no pedaling, yet they launch out faster. This isn\u2019t magic; it\u2019s timing that lets the ground do positive work on you. This reciprocal motion between the bike and the rider is called pumping, evident in three places: rollers, banked corners (berms), and jumps. This article focuses on the physics in berms and a recent model by Golembiewski and colleagues that computes an optimal pumping rhythm through corners. We finish with brief notes on extending the same logic to rollers and jumps.<\/span><\/p>\n

\"\"
Fig 1: Rider pumping through a berm at UCI World Championships (Velosolutions Global, 2024)<\/span><\/figcaption><\/figure>\n

The Basic Physics in a Berm\u00a0<\/b><\/h3>\n

The ground must push hard on the bike to bend its path towards the center. That \u201cheaviness\u201d is the normal load N. A compact way to sketch the load you feel (or the \u201cheaviness\u201d) is:<\/p>\n

\"\"<\/p>\n

The first term is gravity on a bank with tilt \u03b2 , the second term is the centripetal demand of the turn (speed v, radius R), and the third term is what you add by moving your body normal to the surface (a rider)a: positive when you compress, negative when you unweight). Even if the radius R stays roughly constant through the main arc, N ramps up when you go from straight to arc (entry) and drops when you go from arc back to straight (exit). Those ramps are the windows that matter, when a sliver of the ground\u2019s reaction force points forward along the bikes path (T). The instantaneous power is roughly P=Tv. You use this to gain speed.<\/p>\n

The bike has two wheels, splitting the pumping motion into two time frames: a short <\/span>bar press as the <\/span>front hits the entry ramp, then a short <\/span>pedal press as the <\/span>rear reaches it. Those two brief pulses create two small forward pushes per berm. Note that this isn\u2019t conservation of angular momentum (mvr) because the ground is doing external work but applying compressive forces at the right time.\u00a0<\/span><\/p>\n

Why this matters. This turns \u201cpump the berm\u201d from a vibe into a <\/span>repeatable rule you can coach, measure, and design for: press twice in the entry window, glide out, and you bank real, compounding speed\u2014no pedaling required.<\/span><\/p>\n

Inside the Research: A Two-Mass Model on a Banked Ribbon<\/b><\/h3>\n

The paper starts with a cartoon model<\/span>\u00a0where the <\/span>bike and the <\/span>rider are represented by two points\u2014centers of mass <\/span>xb<\/sub> and xr <\/sub><\/span>\u2014 joined by a <\/span>massless link of length <\/span>l(t)<\/span><\/p>\n

\"\"
Fig 2: Simplified Bike & Rider Model<\/figcaption><\/figure>\n

To give these points a world to live in, they build a 3D <\/span>banked surface, called S, using a set of parametric equations:\"\"<\/span><\/p>\n

Think of g as a recipe that turns the pair \u201cwhere you are around the track (\u03a6)\u201d and \u201cwhere you are across the bank (\u0398)\u201d into a 3-D position.\u00a0 Rather than let the bike wander anywhere on S, the authors choose a riding line by prescribing as a function of \u03a6.<\/p>\n

\"\"<\/p>\n

Subsequently, the author derives a position equation for the bike\u2013rider system that depends only on \u03a6 \u2014 <\/span>the progress angle around the banked turn\u2014under the riding line assumption that the rider holds an inner line on the straights and shifts toward the outer (higher) line near the apex.<\/span><\/p>\n

\n
\n
\"\"
Fig 3: Visualization of Riding Path<\/figcaption><\/figure>\n

\"\"
Fig 4: Two-mass model on torus surface<\/figcaption><\/figure><\/figure>\n<\/div>\n

To simplify the problem, the author also introduces an <\/span>upright constraint (Fig. 4): this means the imaginary line between the bike and the rider is always perpendicular to the track surface.<\/span> The movement of the rider will only be orthogonally, no fore\u2013aft lean\u2014so l(t) is exactly \u201chow much you squat or extend\u201d relative to the bank. Under that constraint, an explicit expression for the rider position (g\u0303) is derived.<\/span><\/p>\n

\"\"<\/p>\n

This equation takes \u03a6 <\/span>\u2014 the progress angle around the banked turn, and l (the distance between the bike\u2019s COM and the rider\u2019s COM) as input, and outputs a point in 3D space.\u00a0<\/span><\/p>\n

Setting up an Equation of Motion<\/h3>\n

The authors model the bike\u2013rider system with positions that vary over time. The bike<\/em> position is xb<\/sub>(t) and the rider<\/em> position is xr<\/sub>(t). Velocity is the time derivative of position (how fast the points move), and acceleration is the time derivative of velocity. A single \u201csquat\/extend\u201d degree of freedom along the surface normal is captured by the body\u2013bike separation l(t). In everyday terms, l\u0307 \u00a0is how quickly you are moving up or down, and l\u0308 is how hard you accelerate that motion. This variable l\u0308(t) is the core of the study \u2014 it becomes the control input in the simulation. From the position formulas, the paper computes the speeds (kinetic energy)
\nand heights (potential energy) of both masses:<\/p>\n