Center of Gravity as Performance Art

Before you read this blog, head over and watch this video.  Sorry, I tried to embed it, but it is a really long video.  If you’re short on patience, get the general idea, then go to 6:38 and watch to the end.

See you back in a moment.

OK, pretty cool, huh?  Nine times out of ten, when someone sends me a video and asks me the physics behind it, I have to burst their bubble and tell them there’s a trick somewhere and the video isn’t actually “real”.  (There are no actual talking animals as far as I can tell.)  This video came from @88marty88 — and it’s a great demonstration of a concept you hear talked about all the time in racing, which is center of gravity.

Center of gravity (CG) and center of mass (CM) are the same thing in a uniform gravitational field — which is usually the case here on Earth.  I’ll use them interchangeably because I can never remember which one I decided to use.  Or I may even use them simultaneously.

CMFeather

The CG/CM of an object is the point at which an object balances perfectly in all three dimensions.  (This cartoon illustrating the concept is NSFW.)   If you have a meterstick, the meterstick will only balance if you place your pivot at the 50-cm mark.  That is it’s center of gravity in the dimension along the meterstick.

In the still at right (which is from about 9 seconds in), the woman is balancing the feather on her forefinger.  She moves it back and forth and finds the spot where it stays balanced.  This is the CM.

It’s important for her to know where that is because the key to balancing something is that you have to support it over it’s CG.   A system is stable as long at its CG/CM is within its base of support.  Stand up and lean forward.  At some point, your CG/CM will extend past your feet and you will fall on your face.  Hopefully you are paying enough attention that you catch yourself before that happens.  If you were dancing or ice skating and your partner wanted to balance you with one hand, he/she would have to place that hand such that a line running through the support point also goes through your CG/CM.

CMFeather-2

Once the performer knows the CM/CG of the feather, she is ready to use something  else to balance the feather – in this case, a stick.  Note that the sticks are not sticks you’d find fallen from trees.  They have a  specific shape:   very thick (massive) on one end, tapering to almost nothing on the other end.  If a stick were uniform, it’s CG/CM would be halfway along its length; however, when the mass isn’t distributed uniformly, the CG/CM ends up being closer to the end with more mass.  In the case of the first stick, that’s about 2/3 of the way from the skinny end.    There’s a distinct reason for doing this.

She balances the feather at its CG.  Adding the feather to the stick changes the stick’s CG – not by much, but by the time she’s gotten to the last stick, all that weight will add up.   She doesn’t put the feather all the way at the end of the stick.  It’s about 1/4 of the way from the smaller end.

Next, she feels for the CG/CM of the stick/feather combination  (about 35-40 seconds in is a good place to see) .  When she balances stick 1 on stick 2, the place where stick 2 must support stick one is – you guessed it – the CG/CM of the feather/stick 1 combo.

I’ve tried to show the first four steps below.

 

CGFeather

 

You can do something similar at home in one dimension (which is much easier than what the performer does in the video.)  Get a bunch of books.  Hang one a little over the table, so it just balances.  Now put a second book on.  The second book will make the first book fall — BUT if you pull the first book back just a little, both books will be stable.  You can get quite the stack of books going if you’re careful.  I have a short attention span and my colleagues were starting to wonder what the heck I was doing, so I stopped at five.

It works as long as the cumulative center of gravity remains over the desk.  The minute I slide a book out too far, the CG extends past the desk and the whole thing tips.  CMBooks

You can take some hints from the video if you want to build your own tower of books. She uses shorter sticks at the beginning.  As she adds sticks, she needs larger sticks to keep the CM/CG within the balance point.  If you used small books on bottom (your first “sticks”), you wouldn’t be able to extend as far as if you used larger books on the bottom.

Now books are big, clunky objects, and stacking them this way, you’re really only worrying about the CG along the desktop direction.   (The books aren’t suddenly going to rotate out of the picture!)

The performer in the video is balancing the CG essentially in two dimensions.  The curvature of the materials makes it easier for things to stay put.  That lowers the CG in the up-down direction and low CGs are  pretty much always good when it comes to balance.

It would be interesting to know how heavy the materials she was using are – are they like balsa wood?  Specially made for this very purpose?   If you haven’t watched the end of the video, do so before reading on.

At the very end, she removes the feather and the entire thing tumbles. If you have the largest stack of books you can make and then you nudge the bottom one a few millimeters out, your book stack will collapse two.  That’s how sensitive balance is.

Now… just because it’s basic physics doesn’t mean it’s simple.  The talented acrobats you see in shows like those by Cirque du Soleil, for example, have excellent senses of balance, flexibility and stability.  Understanding the physics doesn’t mean you can turn around and do it.

Plus… I’d probably have to give up coffee for a few days beforehand and we know that’s not going to happen…

 

The Flap over Roof Flaps

Why Roof Flaps?

Roof flaps (the invention of which I detail in my book The Physics of NASCAR) help keep cars on the ground.  This is necessary because of Bernoulli’s law, which says basically that:

  • Faster-moving air exerts less pressure.
  • Slower-moving air exerts more pressure.

A wing develops lift because the air flowing under the wing moves slower than the air going over the wing. That creates more pressure under the wing than over the wing, which generates a net force upward.  That’s a good thing for an airplane.  Not so good for a race car.

A NASCAR race car is pretty stable when airflow goes from the nose to the tail.

The problems start when a car turns sideways because a sideways racecar looks a little like a wing.  Air flows easily over the roof of a sideways racecar. It stays attached to the car’s surface for a long time, and that creates a low pressure region on the top of the car. A little air gets under the car and all of a sudden, the car is flying.

If this happened all the time, you’d engineer the car to prevent it from happening – except whatever you engineered would slow down the car all the time.  Since this is only a problem when a car rotates(i.e. yaws),  you need a solution that only becomes active when the car is yawed.

The idea is to get the air to slow down when it goes over the roof, which increases the pressure on the top of the car and decreases the lift.   As shown at left, the roof flaps are flaps of metal that are normally flush with the roof. When the pressure on the roof gets low enough, the pressure differential between the underside of the flap and the top of the flap causes the roof flap to pop up.  The pop-ed up roof flap slows the air going over the top of the car, increasing the pressure and keeping the car on the ground.

Cars have two roof flaps(which are more appropriately called “hinged air deflectors”).  One runs along a line from left to right and one is angled at 45 degrees to the first, as shown in the figure  (which comes from the original patent #5374098) and is from the pre-Gen-6 car.

The detail of the roof flap is shown at right (again, from the pre-Gen-6 version).  It’s a one-piece assembly made of carbon fiber composite.  The tethers, which are the strings running through the bottom of the tray and through the flaps, are made of a superstrong polymer called Vectran that stops the flaps from relying entirely on their hinges to prevent being ripped off the car when they stand up at 190 mph.  It’s a purely mechanical, deceptively simple design that works pretty reliably and doesn’t have a lot of moving parts.

Gen-6 Roof Flaps

Roof flaps were re-designed for the Gen-6 car.  The old roof flaps were 8″ x 12″.  The new ones are closer to 10″ x 18″.  Larger roof flaps slow down more air molecules than smaller roof flaps.  They are lighter, deploy faster and they have little fabric parachutes to improve their ability to slow down the air running over the top of the car.   The photo below is from one of my favorite magazines, Circle Track – check out their article to learn about other details of the Gen-6 car.  Compare the first diagram and the photo below.  See how much further over to the side of the roof the roof flaps run?

2013CircleTrack_42RoofFlap

What are Roof Flap Spacers?

Roof flap spacers are metal disks that sit in the tray and give the roof flaps something to rest on so that they remain level with the roof surface.  There are two spacers for each flap, making a total of eight spacers in the car.

RoofFlapGate

Teams buy roof flap assemblies from Roush-Yates.  The picture below is again the COT assembly, and the picture is from the Roush-Yates catalog.  The assembly costs $1130.00.   The key word here is assembly.  They come assembled and the idea is that you  drop them into their hole in the roof of the car.  COTRoofFlapPicture

And you don’t mess with them in any way before you drop them into the car.

The whole ‘roof flap spacer-gate’ thing (see Dustin Long’s MRN article for a picture of the confiscated parts) appears to be a simple case of teams shaving down components to save weight at the top of the car.

I know!  Four small cylinders – how is that going to change anything?  Remember that teams are scrapping for any advantage they can find.   Here’s the physics:

  • The grip on each tire is proportional to how hard the tire is being pushed into the track.
  • The force pushing each tire into the track is a combination of mechanical downforce (i.e. the weight of the car) and aerodynamic  downforce (the force of the air pushing down on the car)
  • The force on each tire changes as the body rolls during turns.  Accelerating out of a left turn transfers the weight of the car toward the right rear, so you lose grip on your left front tire.
  • The amount of weight that shifts during a turn depends on the height of the car’s center of gravity.  The higher the center of gravity, the more weight shifts and the more change in grip you have on your tires.

Teams have been using carbon fiber for things like dashboards in an attempt to keep the center of gravity as low as possible.

Note:  @DGodfatherMoody reports that each of the spacers was lightened by about 3 oz.  There are 8 spacers on the two roof flaps, so you’ve got 24 oz or about a pound and a half lighter.  That’s significant!

What are the Penalties Going to Be?

This is a hard one to predict.

  • You can’t say that it didn’t given anyone a performance advantage because of the above argument.  Maybe not a huge performance advantage, but come on – if it wasn’t going to make the car faster, why would you try it?  No one seems to think that the modified spacers had anything to do with aerodynamics.
  • The rule book says “The hinged air deflectors must be NASCAR-approved and obtained only through NASCAR-approved sources. The hinged air deflectors must be installed as specified in the instruction sheet supplied with the hinged air deflector kit.”  …and I’m guessing the instruction sheet doesn’t tell you to shave weight off the spacers.  Or do anything with the spacers.  It’s going to be hard to argue that you were working in the grey area with this.
  • It’s a safety device.  NASCAR doesn’t take kindly to monkeying with safety devices — even when the modification doesn’t impact the function of the safety device.
  • NASCAR has been increasingly grumpy about people trying to skirt the rules.  Penalties have been escalating and what might have been tolerated at the start of the season might have the hammer come down at the midpoint.
  • NASCAR has had an unprecedented number of penalties reduced by the appeals panel this year.  The last couple appeals outcomes may impact their thinking on the magnitude of the penalties.

If it were me, it would be a roll of the eyes and a shake of the head and telling the crew chiefs that if we catch you doing it again, you’re going to be watching the next couple of races from in front of the television.

Move along folks… nothing here to see, I think.

Parts of this blog were adapted from a blog previously published on the now defunct stockcarscience.com on 4/26/2009.