No, He Didn't

Am I on the ring road? Stunt driver defies gravity on the world’s biggest loop-the-loop

He didn’t defy gravity — I’m sure it was there the whole time.

If stuntman Steve Truglia had been too timid in his acceleration, his yellow Toyota would have reached the top of the track and dropped like a stone.

Not quite. If his speed was insufficient, he would not have reached the top. But the car would have dropped like a stone.

The Toyota had to be travelling fast enough that the centripetal force generated by its circular motion ‘offset’ the downward pull of gravity. This required the stuntman to enter the loop at exactly 37mph, immediately change out of gear and slow to 16mph as the vehicle swung round the top.

Well, no. The centripetal force is the gravitational force in the limit of the slowest speed that allows you to complete the loop, and the speed will naturally decrease as kinetic energy is converted to potential energy. Since the loop is 40 ft tall, we can actually calculate this. An object entering the loop and rising 40 feet to be traveling at 16 mph must be going 38 mph as it enters. The article says 37, but car is a little off the ground, so the actual change in potential energy is smaller. (The actual change in height is 37.4 feet using those numbers, putting the CoM a little over a foot off the ground. Close enough)

The downshifting isn’t there to slow the car down — the only thing the engine needs to do is compensate for losses. The downshifting is because the car will slow down, and you don’t want it to stall as the result of being in the wrong gear. An ideal car (of which a Toyota does not qualify) could simply coast after entering the loop. It’s entirely possible to enter the loop at a slower speed, but have the engine make up the additional energy needed while in the loop, but that would not have been the safe move from the he-doesn’t-so-much-loop-as-plummet angle .

And, from a physics point of view, he could have gone faster. 16 mph gets you about 1g of downward acceleration, i.e. you are basically in freefall under that scenario. The numbers don’t quite jibe — even when I use the smaller radius from above, the acceleration is a little lower than 1g. So undoubtedly some rounding went into the story already. Going faster would just mean that the track was exerting some force on him while at the top.

As far as the danger of blacking out, that’s why he wanted to be going near the minimum speed at the top, because near the bottom is where he would pull the most g’s — about 5 of them, at that speed, assuming the track is circular and not flattened to reduce the force.

Physics Malpractice

Via physics and physicists I see a story about how golf can be hazardous to your hearing. And the story botches the physics. (I don’t know if it’s the journalist or from the original journal article)

The coefficient of restitution (Cor) of a golf club is a measure of the efficiency of energy transfer between the golf club head and the golf ball. The upper Cor limit for a golf club in competition is 0.83, which means that a golf club head striking a golf ball at 100km per hour will cause the ball to travel at 83km/h.

Well, that’s just wrong. The Cor tells you about the kinetic energy, so it won’t be the same for the speed, because KE depends on v2. i.e. if a ball is dropped from 1 meter and bounces, returning to 0.83m, the impact speed is ~4.4 m/s and the return speed is ~4.0 m/s, which is 0.91 of the speed.

Another problem is that the mass of the clubhead is not the same as the mass of the ball. Even if the Cor applied to speed, the statement is incorrect. In the limiting case of Cor=1 and the ball’s mass being negligible, the ball would leave at twice the clubhead speed.

The actual equation is v = u*(1+e)/(1+m/M)

v is the ball’s speed, u is the clubhead speed, e is the Cor, m is the ball’s mass and M is the clubhead mass. (This is trivially derived using conservation of momentum and balancing the kinetic energy equation to account for the loss) Using e = 0.83, and assiming the M=4m, we see that v = 1.46u

Update — This is using a definition of Cor on terms of energy. I couldn’t find how the USGA was defining it when I was composing the post, but further research (and noted in the comments) indicates that it is indeed the fraction of the speed retained after the collision. That changes the details of the analysis, but the article’s numbers are still wrong — the ball’s speed is larger than the clubhead speed. I still haven’t found a mathematical definition of how the USGA applies this to a golf club

That makes e in the equation the square of the Cor (so e = 0.689), which means that the ball leaves the clubhead at v = 1.35u

Wrong Numb3r

This was a nit that may have bothered only me (and my ilk. My ilk is somewhat sensitive to such things). In this past week’s episode of NUMB3RS, there’s a scene where Liz and Nikki go to arrest some 350-pound badassMF™. One of them tries some FBI-fu on him, is thwarted, and the other (I forget which did which) grabs a fire hose and knocks him over with the jet of water and a cliché. Except that momentum is conserved, or is supposed to be. The impulse from the water leaving the hose should knock the person holding it back, and given that either of these characters has somewhere around a third of the mass of the target, should have not been able to easily wrangle such an instrument of havoc.

This is similar to the magic shotgun, that is recoil-free to the wielder, but is able to knock the target a meter or so backward when struck.

Well Blow Me Down

Over at Good Math, Bad Math, Mark has a takedown of a device purported to move directly downwind, faster than the wind. Wind-Powered Perpetual Motion (and Dave Munger thinks he’s wrong.)

Here’s the video

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The objection is simple: when you are traveling at the wind speed, there is no more wind in the cart reference frame, so there’s no force. The treadmill analysis is flawed.

If you’re testing a wind powered vehicle, then in a closed, windless room, putting the vehicle on a treadmill moving at 10mph is not the same thing as putting the vehicle on a stationary surface in a 10mph wind.

By putting it on a treadmill, you haven’t recreated the real-world situation — you always have your wind, and the treadmill doesn’t remove that. You never test the condition of having the wind relative to the cart drop to zero. So while it’s not faked, it’s still a sham.

It shouldn’t be hard to engineer a device such that the wheels rotate faster than the propeller, i.e. whatever the propeller’s rotation rate is for a wind of speed X, the wheel edges move faster than X. Since the wind is always present, the cart will move forward on the treadmill moving at X. Even uphill.

My question is this: if this works, at what speed does the cart stop accelerating?

UPDATE: Or with no wind present, as in the test (On the first viewing I thought they had a fan turned on) what you’re doing is converting treadmill kinetic energy into propulsion by turning the propeller. But you don’t need to have much propulsion to move forward, even uphill. Not a valid test.

Update, Mark II. See the comments — I was viewing this from the mistaken notion that the propeller was acting as a turbine while on the ground and at low speed, which isn’t the case.

This has the implication, I think, that the cart must have enough mass to ensure that the propeller acts as a propeller. My question of what the maximum speed is still stands, because I’m sure it involves fluid mechanics and that’s not something I’ll win should I tangle with it.

That's Dr. Time to You, Pal!

Meet the world’s director of time

An interview with Dennis McCarthy, who is the Director of the Directorate of Time (or was at one point; I’m not sure how his retirement and subsequent resurrection affected the job title)

Though the BBC filmed in the lab, none of that footage made it into the embedded clip. Perhaps there’s footage in the show that’s airing on BBC 2, as I type this. I’ll have to check it out.

More than anyone, Dr McCarthy appreciates the need for the world’s population to be synchronised. But for those who don’t spend their working day checking atomic clocks, why is knowing the time so important? Think for a moment about how the GPS satellite navigation system works.

There is a network of over 30 satellites orbiting earth that broadcast a high-precision time-stamp down to the GPS system in your car.

These signals travel at the speed of light, which is very nearly one foot every thousand-millionth of a second – or one nanosecond (for the more metrically minded, that’s around 30cm, which is far less elegant. If there is a God, he built the universe using imperial measurements).

If that last part is true, God has a hell of a sense of humor.

The was one part of the embedded video that made me cringe, and that was the depiction of the Bohr-ish atom (with wavy orbit lines — is that supposed to make it all better?) and the electron making a transition between them. But in that representation, those are the levels described by the principle quantum number, and the transition of microwave clocks is in the spin state of the electrons, oscillating between spin-up and spin-down (whose energy degeneracy is broken because of interactions with the nucleus, which also has spin, and thus a magnetic moment) And the notion that you’re looking at radiation emitted by the atom is true in an active maser but not a passive standard like a cesium or rubidium clock — in those you make a separate measurement of the atom to tell you what state the electron is in.

(I don’t know if it’s a permanent link, but in the “In Today’s Magazine” column there’s Call him Mr Time . Hence the title, though I can’t actually envision Dennis saying that to anyone)