Saturday, 19 August 2017

Jumping without slipping


The image here is of a leafhopper. These leafhopper and their close relatives the froghoppers are capable of amazing jumping feats.

Philaenus frog-hoppers have relatively short hind legs (66% of the body length), are able to accelerate in less than 1 ms to take-off velocities of up to 4.7 m s−1, when jumping from high-density foam. In comparison, Aphrodes leafhoppers (pictured here) have longer hind legs (84% of the body length), take longer (4.4 ms) to accelerate and achieve take-off velocities of up to 2.9 m s−1 on high-density foam.

On a rough substrate such as foam, spines or claws on the hind legs may be able to grip, but they may not be able to engage with smooth surfaces, like glass.

This is because insects also cannot rely on classic friction alone,

Their take-off angle α = tan−1(Fnormal/Fshear) = tan−1(1/μ) is limited by the friction coefficient μ (Amontons' law of friction: Fshear = μ Fnormal, where Fshear is the force parallel to the surface and Fnormal the load normal to the surface). Friction coefficients μ for rigid, dry surfaces are typically less than 1. Assuming μ = 0.35 (like we measured for beetle claws on glass), insects could only jump upward with steep take-off angles α > 70°. To jump forward, insects require significantly higher friction coefficients (μ). So how do they do it?

We tested this idea and it turn out, some insects can, but some can't. Watch this video of the shorter legged froghoppers, with their higher acceleration trying to jump from glass.


That froghopper is getting nowhere quick. Its legs slip and cause it to spin, forward uncontrollable  (and hilariously) at a high angle predicted by our model.

But froghoppers can jump from glass. And they do so using these soft adhesive pads, which were different to those seen in other insects we looked at. Furthermore, when we tried to test the pads to see how much friction they can create (see our method below), the forces were too low to account for their take off velocity and angle.


This was puzzling since we really couldn't explain the final jump velocity, and the forces the leafhoppers were producing on glass were too low to produce the observed take-off velocity. 
One day i was sitting in the lab explaining the problem to my then supervisor Walter Federle in his lab, in the old Cavendish laboratories at Cambridge, and he asked me to show his how the experiment ran. We went through a few trials, and we were both perplex as to where the forces were coming from, was there something wrong with our system? When testing the force, we like to move the glass plate to a new spot each time so we don't get a build up of adhesive fluid, which lowers adhesion (a whole different study!) - so i manually changed some settings to move it to a clean sections. 

Yet I must have changed the wrong setting since the plate moved much faster than i anticipated. Normally we used quite slow speeds, cause the whole setup, including our poor tethered insects, is quite fragile, and the robotic arm could easily crush it all (as work with the occasional undergrad student has taught me). But this time sometime peculiar happened. The force we got back we much high, much much higher. We performed some quick back of the envelope calculations (though should now be called on the paper towel calculations - since nobody has envelopes lying around anymore) - and they were high enough to explain the jumps we had seen before. 
More over the contact area of these weird pads went from looking like this during a slide.


To this





So we had solved our problem, and in doing so discovered that these new pads were actually velocity dependent. In other words the amount of friction produced increases with the speed at which they are sliding across the surface.

Very important if you want to avoid slipping while jumping from smooth surfaces. 

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