Peer-reviewed literature: the math behind pumping

Despite the fact that, at present, skateboarding is one of the most popular forms of sports activities, the dynamics and stability of the motion of a skateboard have not yet been seriously investigated […]

(Alexander Kuleshov, 2007)
Velocity and average velocity (Ispolov & Smolnikov, 1996)

So it exists! The pumping motion is described by these Russian mathematicians (and I must assume, avid slalomers). The math exceeds me by far, but someone, somewhere, sometime might find this helpful, hopefully.

Ispolov, Y. G., & Smolnikov, B. A. (1996). Skateboard dynamics. Computer Methods in Applied Mechanics and Engineering131(3), 327–333.

(Ispolov & Smolnikov, 1996)

Pumping described mathematically (Ispolov & Smolnikov, 1996)
Pumping described mathematically (Ispolov & Smolnikov, 1996)

Other notable papers:

Hubbard, M. (1979). Lateral Dynamics and Stability of the Skateboard. Journal of Applied Mechanics46(4), 931–936. [this is widely cited as the first effort to describe a skateboard mathematically; I’ve tried to explain before that there’s always a point with 0 lateral velocity (0 “turn”) and here this fact is shown in the first page as elementary of the model; he also shows a tilt-turn equation, but it’s wrong]

Österling, A. E. (2004). On the Skateboard, Kinematics and Dynamics (SSRN Scholarly Paper No. ID 1823272). Rochester, NY: Social Science Research Network. Retrieved from [this BSc math student says Dan Gesmer personally gave him Hubbard’s paper; he then went on to discover and prove the equation between tilt (lean) and turn of axles; I thought I was the first one in the universe and I could publish it some day and become famous (how presumptuous?)]

Kremnev, A., & Kuleshov, A. (2010). Nonlinear dynamics and stability of the skateboard. Discrete and Continuous Dynamical Systems3(1), 85–103. [these two are cited by others as getting the tilt-turn function first – Österling did, though he hadn’t published that in a peer-reviewed journal; the authors, of course, explore and prove other stuff too which I cannot even comprehend]

Rosatello, M., Dion, J.-L., Renaud, F., & Garibaldi, L. (2015). The Skateboard Speed Wobble. 11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control6, 1–10. [this paper is probably what you should read on speed wobbles, instead of Carver’s musings; however, they assume rake to be 0, so it’s perhaps not complete; also, they say that bushings determine “a restoring torque between the wheel-set and the board, proportional to the tilt angle” which is not true, as I showed here]

Varszegi, B., Takacs, D., & Stepan, G. (2016, January 19). Skateboard: A Human Controlled Non-Holonomic System. ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. [this is a conference paper and it deals with stability and speed wobbles]

Kunesch, M., & Usunov, A. (2010). Tic-tac: Accelerating a skateboard from rest without touching an external support. European Journal of Physics, 31(4), S25. [the title of this one is self-explanatory; they expand on Ispolov & Smolnikov’s (1996) paper]

Endruweit, A., & Ermanni, P. (2002). Experimental and numerical investigations regarding the deformation-adapted design of a composite flex slalom skateboard. Sports Engineering, 5(3), 141–154. [this is for the deck geeks; deals with the properties and behavior of a composite deck under slalom]

(Varszegi et al., 2016)

A couple of sociological papers:

O’Connor, P. (2018). Beyond the youth culture: Understanding middle-aged skateboarders through temporal capital. International Review for the Sociology of Sport, 53(8), 924–943.

Willing, I., Bennett, A., Piispa, M., & Green, B. (2019). Skateboarding and the ‘Tired Generation’: Ageing in Youth Cultures and Lifestyle Sports. Sociology, 53(3), 503–518.

Robinson, R., Patterson, I., & Axelsen, M. (2014). The “Loneliness of the Long-Distance Runner” No More. Journal of Leisure Research, 46(4), 375–394. (while not related to skateboard, it offers a pretty robust theoretical framework for describing the distance skating scene)

2 thoughts on “Peer-reviewed literature: the math behind pumping

    1. I’m just glad you found it useful! Please do share it with anyone you think might appreciate this list.
      I try to keep it updated, so do check back at some point.
      I actually checked for new papers just yesterday, but there’s nothing extremely interesting out. Just a couple more papers about speed wobbles and one about rip-sticks 🙂

Leave a comment

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.