Thursday, 17 January 2013

Hefting for a Maximum Distance Throw

From the task dynamic analysis of throwing for maximum distance, we've identified the fact that for a given release angle and maximum release velocity, there is an object whose size and weight optimises the distance it will travel when thrown. Can people perceive this combination ahead of time? More specifically, can people identify the object which affords throwing to a maximum distance, and if so, how?

Bingham, Schmidt & Rosenblum (1989) is the first paper investigating this question. It is a bear of a paper; I've stripped a lot of the methodological detail out in my summary so I can focus on the bigger picture. That bigger picture is this; Bingham et al first check whether people can identify objects that afford throwing to a maximum distance by hefting them ahead of time (they can). They then investigate the kinematics of hefting to identify an invariant relation in the timing of the wrist and elbow velocities and relate that invariant to the dynamics of throwing (specifically how it maximises the transfer of kinetic energy from the torso muscles to the projectile). They propose that using this invariant reflects a smart perceptual solution (Runeson, 1977) to the problem of selecting objects to throw to a maximum distance - future work (Zhu & Bingham, 2008) will actually show that this specific smart mechanism doesn't hold up, although the replacement is smart too.

Perceiving object affordances for throwing
Bingham et al created a set of objects varying in size and weight and asked people to heft those objects to identify, within each size, the weight they thought they could throw the farthest. You've probably done this yourself at some point; standing on a rocky shore, holding rocks until you find that one that feels just right. People found the task very natural, and chose their objects with confidence. The main result; as size increased, people preferred heavier objects. (This, by the way, looks a little like the pattern you see in the size-weight illusion, and the connection between that 'illusion' and throwing seems to not be an accident; Zhu & Bingham, 2011).
Figure 1. The weight of preferred objects as a function of object size
They then had some of those people throw all the objects, and they measured the actual distance each object travelled. Smaller objects went further, and on average people threw the objects they preferred the farthest. They had indeed perceived the affordance for maximum distance throwing via hefting.

Figure 2. Distance thrown as a function of size (I = smallest, IV = largest) and preference
So the initial answer to the question is 'yes'. People can choose the optimal objects ahead of time, and both their judgments and their performance depend on both the size and weight of the object (as we would expect from the task analysis). Bingham et al then explored a potential mechanism by which hefting was providing information relevant to throwing.

The kinematics of hefting

The data above showed that people were perceiving a relation between size and weight that was related to throwing. Specifically, they were perceiving the maximum of the size-weight-distance function. Weight (or more precisely, mass) is a dynamic property. We perceive dynamic properties via their kinematics, the motions they produce; this is the perceptual bottleneck. So people aren't detecting weight, per se, but some kinematic consequence of the size and weight of the ball during hefting that is specific to the dynamics of throwing.

Maximising distance means maximising release velocity, and this means maximising the kinetic energy delivered to the projectile. Throwers generate force in their large torso muscles, but then have to transfer that energy to the projectile as efficiently and as quickly as possible. The system adopts two smart solutions. Efficiency comes from careful timing of the motions of the limbs so that the force generated by the muscles is used to accelerate lighter and lighter limbs with minimal loss, producing faster and faster movements. Speed comes from storing energy in tendons and then releasing that energy with a fast snap at the wrist (this is what tendons are for). Hefting and throwing both exhibit these kinematic properties, at least from the elbow down, and this overlap is the best place to go looking to see how hefting an object can produce information about that object's affordances for throwing. Experiments 3 and 4 therefore investigated what changing the size and weight of objects did to these wrist and elbow kinematics, looked for invariant features of these kinematics when hefting preferred objects and related that invariant to the dynamics of throwing.

As object size increased, the preferred weight increased (Figure 1). Experiment 3 established that increasing object size increased the stiffness about the wrist joint by altering the amount of tendon available for prestretching and energy storage. Bouncing an object in your hand can be modeled as a harmonic mass-spring oscillator, and increases in stiffness increase the preferred frequency of such oscillators. In other words, if you just increase the object size you'll end up wanting to bounce faster and faster - you will perturb the timing of the wrist motion, which will interfere with the task of preserving the timing between the wrist and other limb segments that transfers energy efficiently. If you also increase the mass appropriately, however, you can preserve the timing over changes in object size. Perhaps hefting an optimum object produces a specific oscillation timing? If so, this invariant kinematic pattern might therefore specify throwability to a maximum distance.

Experiment 4 therefore looked at how changes in object size and weight affected the timing of flexion and extension in the wrist and elbow. Changing object size altered the timing in the wrist; changing object mass altered the timing in the elbow. To preserve an invariant pattern of timing between the wrist and elbow, size and weight therefore needed to change in particular ways in relation to one another. Size and weight do vary in particular ways for preferred objects, and hefting these produced an invariant timing between the wrist and elbow. This invariant pattern is therefore a candidate to be information about the throwing affordances of the object which is available during hefting. So what dynamic property is it specifying? 

The goal of controlling the timing between the limb segments is to efficiently transfer energy from the trunk muscles to the object and maximise the kinetic energy of the projectile, to maximise release velocity. The equation describing how the kinetic energy is generated contains three terms (appendix B): wrist velocity squared, elbow velocity squared and the product of these two values. These values ebb and flow over time. Maximising the kinetic energy means aligning peaks in these values as closely in time as you can so they add up. Hefting preferred objects produces very closely aligned peak values for these three terms; hefting non-preferred objects alters the timing and disrupts the alignment. 

So the chain of events is this (Bingham et al suggest): hefting preferred objects produces a particular invariant relation in the timing of wrist and elbow motion. Preserving this timing relation as objects increase in size requires an increase in object mass to offset the size-induced increase in wrist stiffness and the related changes to the spring properties of the wrist. The particular invariant timing produced by the particular size-weight combinations that define preferred objects maximises the kinetic energy that can be transferred to the object, which in turn maximises the release velocity and therefore the distance.
The kinematics of hefting a preferred object therefore specifies a throwing related dynamical property of the objects, and people are sensitive to that information and what it means. This smart perceptual mechanism is the target of the next paper I'll review, Zhu & Bingham (2008).

Bingham, G., Schmidt, R., & Rosenblum, L. (1989). Hefting for a maximum distance throw: A smart perceptual mechanism. Journal of Experimental Psychology: Human Perception and Performance, 15 (3), 507-528 DOI: 10.1037//0096-1523.15.3.507 Download
Runeson, S. (1977). On the possibility of "smart" perceptual mechanisms. Scandinavian Journal of Psychology, 18 (1), 172-179. Download

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(4), 929-943. Download

Zhu, Q. & Bingham, G.P. (2011). Human readiness to throw: the size-weight illusion is not an illusion when picking the best objects to throw. Evolution and Human Behavior, 32(4), 288-293. Download


  1. Nice summary. Thanks! You make me feel bad about how long winded and detailed my summaries of F&P vs. TSRM were... At any rate:

    "Changing object size altered the timing in the wrist; changing object mass altered the timing in the elbow."

    This seems like it would lead to a clear set of experiments restricting elbow movement and holding hand-grip-size constant. I assume those have been done?

    1. I'm trying to make this work accessible; Geoff is damned thorough though so it's hard! :)

      We've never manipulated the person; Geoff and Arthur have done a bunch with the varied objects and the three of us are doing targeted stuff. There is MUCH to do and I want to write a grant for it this year if I can get access to the lab space I need. Fingers crossed!