Kinematics of Grasshopper Hops - Smarter Every Day 102

[Smarter Every Day theme music]

Hey, it's me Destin. Welcome back to Smarter Every Day. Today I'm at the Tambopada Research Center, it's run by Rainforest Expeditions, and we're gonna calculate the force that a grasshopper uses to jump with.

First thing we're gonna do is we're going to weigh the grasshopper. So this envelope, we're gonna zero our scale, so... and then put the grasshopper in the envelope, so you know force = mass x acceleration, so we are going to figure out the mass of the grasshopper and we're gonna use this high-speed camera to calculate the acceleration of the grasshopper.

So, how much does our... wait we weren't, yeah we were... 0.1 gram? That sound right, Mr. entomologist?

• Sounds about right.

• Alright. Now we gotta measure a length of his leg, so if you can measure any feature that we can get. We'll do this in millimeters.

That's the long skinny one on the back?

• Yep, so that is called the tibia just like with us.

• It's a tibia just like us?

• Yep.

• So what do you have, looks like 15mm?

• Yeah.

(Destin) Got it. [laugh] That was fast, I got it. [music] Camera ready.

• 3.. 2.. 1..

(Destin) Got it.

• Oh yeah!

• Alright, so now we're gonna calculate what its acceleration rate was. We're going to basically plot how fast he went based on that measurement from his femur and his tibia, right?

• Yeah.

• Alright, and we'll figure out how much force a grasshopper leg has. I recorded two high-speed videos of grasshoppers hopping in the Amazon. I'm gonna calculate the acceleration of one, and if you so choose you can calculate the acceleration for the second one. Only take a couple of minutes and I know you're smart enough.

The first thing you're gonna do is download some software called tracker. Links below. All you do is get tracker and you import a video file from the grasshopper hopping. Once you have it in there, now we have to set our scale factor.

All you do is wait till the grasshopper's hopping so that his leg is stretched out in the plane that the camera's looking at. Once you get to that point you simply create the ratio by clicking the gauge length of his leg and setting it to 15mm. After that, you go back to the initial frame.

And at this point, we're going to select a track point about his eye. The reason we use the eye is because it has good contrast with the background. At this point we can set the track point and begin to play the file and create a velocity vs time curve of the grasshopper hopping out of the screen.

Once we have this velocity vs time curve, all we have to do is create the slope of this line and that's acceleration. Derivative simply means slope of the tangent line. That's what we've done here. The derivative of velocity is acceleration.

So once we have this slope of the line you can see right there the acceleration of this grasshopper is just over 400 metres per second squared. Now all we have to do is use force = mass x acceleration and you can calculate the force that a grasshopper pushes against stuff when it hops.

But wait a second. Think about this. We calculated the force that his legs are putting out based on jumping off of a rigid surface. What if he's on grass? I mean he's a grasshopper after all. That grass or a leaf or something would have to push away because it has to give, it's not rigid.

That means the velocity at which he accelerates away when he hops is directly affected by the rigidity of whatever he's hopping off of. I have never thought about that. You probably haven't either. Anyway, so grasshoppers literally live and die based on what they're hopping away from. That's amazing.

OK, if you're not too lazy go grab that tracker software and get that second hop video file from the video description, calculate the instantaneous velocity of that grasshopper as he hops out of the screen, back out the acceleration and then from there calculate the force on the grasshopper legs. Should be pretty fun.

Leave me a comment, tell me what value you get, see if it compares to the first number we got. Ready for grasshopper launch?

(Son) Yes sir.

(Destin) OK, here you go... 5.. 4.. 3.. 2.. 1.. Go.

[bang] [laugh] Try it on the floor this time. Set it up.

OK, this week on Smarter Every Day I'm gonna recommend an audible.com book which is Wicked Bugs by Amy Stuart. You know audible is a sponsor for Smarter Every Day so you help Smarter Every Day out if you go download a free audio book at audible.com/smarter.

Anyway, this one's about all kinds of crazy bugs and how they've interacted with humans throughout the years. You may recognise some of the names of the bugs from Smarter Every Day. Brown Recluse, Brazilian Wandering Spider, things like that.

Anyway, audible.com/smarter and you'll help Smarter Every Day, and you'll get a free audio book. It's really a win-win. You ready for launch?

• Yessir.

• OK, ready? Think you can hit the ceiling this time?

• Yes sir.

• 5.. 4.. 3.. 2.. 1.. Go!

That was good. Anyway, shouldn't you be calculating the acceleration of a grasshopper jump right now? Anyway, audible.com/smarter. Thank you very much for your support. Getting Smarter Every Day. Have a good one.

[Captions by Andrew Jackson] captionsbyandrew.wordpress.com Captioning in different languages welcome. Please contact Destin if you can help.