The Task Dynamics of Throwing to a Maximum Distance

In my last post I went over the formal concept of task dynamics as a way of analysing a task to identify the affordances in that task. This post will examine the task dynamics of projectile motion and relate these to throwing to a maximum distance.This version of the task has been studied in detail over the last few years. There is another version of the task, namely throwing to hit a target (same dynamic, different parameters, therefore same task) and we will get to that later; we're working now on data from this task.

Part of my goal here is to lay out the research programme you should be following, if you want to study anything to do with perception and action. If you are interested in movement, and you aren't doing this kind of analysis as part of your work, then, I will suggest, you are doing it wrong. As we will see in future posts, this level of detail isn't just playing with numbers; a formal understanding of the underlying dynamics governing the task we are studying is utterly crucial if we want to be able to understand what people are doing, rather than simply describe their behaviour. 

Also it's fun :)

Throwing to a maximum distance, from the point of view of physics
Throwing is an example of projectile motion. The dynamics of projectile motion describe how an object moves through space after being given an initial push and then being left alone, other than the effects of gravity - no additional propulsion. That initial push can be anything (being thrown, being shot out of a gun or cannon, being hit by a baseball bat), and the resulting motion looks like this:

Figure 1. The dynamics of projectile motion

The distance travelled by the projectile depends on the object size and weight, the release height, angle and velocity, drag, air density, and gravity. 

For a given object, maximising distance entails selecting and executing a release angle of around 36° (assuming typical air resistance values) and maximising your release velocity. A person will have a maximum release velocity that they can generate. Given this release velocity and angle, the only remaining way to affect the distance is to identify and use an object whose size and weight combination produces the maximum distance for those release parameters. 

1. For a given size, as weight increases, distance will first increase, reach a peak and then decrease. The location of this peak will reflect the relationship between the force imparted by the release velocity and the mass to be accelerated (think about (or better, try) throwing a ping pong ball vs a golf ball, for example).
2. For a given weight, as size increases, distance will first increase, reach a peak and then decrease. The location of this peak will reflect the trade-off between the force imparted by the release velocity and the cross-section of the object, which creates air resistance. 

There is therefore a function that relates size, weight and distance in the world. Each combination of size and weight will produce a different peak distance in this function, and the collection of all possible combinations will produce a surface with its own peak This function maps the affordance property 'throwable to a maximum distance'.

Throwing to a maximum distance, from the point of view of the organism
Embodied perception-action research must always remember that it has to also analyse the task from the first person perspective of the organism (Barrett, 2011). As far as the organism is concerned, the task dynamic variables listed above can be sorted in the following way:

Things to be perceived: object size, object weight, distance travelled
Things to be controlled: release height, release velocity, release angle
Things outside your control: drag, air density, gravity

Perception: The perceptual question is whether people are sensitive to the size/weight/distance function; can they perceive the affordance? Specifically, given objects which vary in size and weight, can people select the one they can, in fact, throw the farthest? The answer is yes (Bingham, Schmidt & Rosenblum, 1989; Zhu & Bingham, 2008) although poor throwers require practice to be able to do so.Learning is critical.

The next perceptual question is how do they perceive this affordance - what is the information? The answer is 'we don't know yet', but recent work has ruled out the inertia tensor as the dynamic property generating that information (Zhu, Shockley, Riley, Tolston & Bingham, 2012). I'll go into these papers in the next few posts. 

The perceptual questions in this task are therefore about perception of object affordances and how they relate to distance. People are therefore perceiving properties of the object (size and weight) measured with respect to the task demands (maximising the distance of a projectile motion throw). This can be expressed in terms of the perceptual equivalent of the real world function mapping size and weight to distance. We will therefore measure the perceptual function using action measures (see below) and relate it to the known world function.

Action: Implementing a given throw requires implementing the dynamics of throwing, and coupling those dynamics to the dynamics of projectile motion. You couple two dynamical systems together by having the output of one feed into the other (and sometimes vice versa). Throwing is a one way coupling, and it is achieved by having the dynamics of throwing produce three values (release angle, release velocity and release height) which can be used as parameters on the relevant variables making up the dynamics of projectile motion. All three of these can be measured, and are action measures of the perception of the object affordances. Such measures are the 'gold standard' when measuring perception-for-action (Bingham & Pagano, 1998).

To maximise distance, the release angle should be approximately 36° and the release velocity should be as high as possible. Release height varies between people but we're finding it remains fairly constant, and it doesn't currently look as if people are actively controlling it. It is therefore a frozen degree of freedom (c.f. Bernstein, 1967). People typically produce suitable angles quite quickly, and are able to do so more reliably with training. With practice, people improve distance by increasing release velocity, and (if they are allowed to see the distance the ball travels) these action improvements come hand in hand with improved sensitivity to the object affordances (Zhu, Dapena & Bingham, 2009; Zhu & Bingham, 2010).

A biomechanical side note: Why is release velocity the hardest parameter to control? It's because high velocities require exquisite timing and control. In order to accelerate a mass to a high release velocity, you must generate a lot of force. This force must be generated in the large, slow torso muscles and transmitted along the arm and to the ball in a kinetic chain. 

Figure 2. An example kinetic chain (for a baseball pitch)

A force of a given amount accelerates the torso a given amount; if this force is then transmitted to the upper arm, this accelerates the arm more because that segment weighs less than the torso. The force is then transmitted to the lower arm and the hand, with the same result: better and better acceleration and higher and higher speeds. This force is then imparted to the projectile at release. 

The efficiency of this force transfer (i.e. how much you lose along the way) depends on the timing of the transfers. If the timing is off, then some of the force is wasted in producing motions that aren't relevant to moving the wrist along the required trajectory. The better the timing, the more efficient the transfer, and you maximise the acceleration of the hand and object. This requires a high level of precision, and while there is some evidence that we come equipped to produce this kind of precise movement (and that this got recruited for speech) we still have to learn how to implement it.

Summary
The task dynamics of projectile motion, considered with respect to the specific version of the task throwing to a maximum distance provides numerous questions for empirical investigation, and the tools to interpret the results. The next few posts will review the empirical work on this task. 


Barrett, L. (2011) Beyond the Brain: How the Body and the Environment shape cognition. New Jersey, Princeton University Press. Amazon.co.uk Amazon.com 

Bernstein, N.A. (1967). The coordination and regulation of movements. Oxford: Pergamon Press.

 Bingham, G.P. & Pagano, C.C. (1998). The necessity of a perception/action approach to definite distance perception: Monocular distance perception to guide reaching. Journal of Experimental Psychology: Human Perception and Performance, 24 , 145-168.

Bingham, G. P., Schmidt, R. C., & Rosenblum, L. D. (1989). Hefting for a maximum distance throw: A smart perceptual mechanism. Journal of Experimental Psychology: Human Perception & Performance, 15(3), 507-528.

Zhu, Q. & Bingham, G.P. (2008). Is hefting to perceive affordances for throwing is a smart perceptual mechanism? Journal of Experimental Psychology: Human Perception and Performance, 34, 929-943. 

Zhu, Q. & Bingham, G.P. (2010). Learning To Perceive the Affordance for Long-Distance Throwing: Smart Mechanism or Function Learning? Journal of Experimental Psychology: Human Perception and Performance, 36(4), 862-875.

Zhu, Q., Dapena, J. & Bingham, G.P. (2009). Learning to throw to maximum distances: Do changes in release angle and speed reflect affordances for throwing? Human Movement Science, 28(6), 708-725.