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Author Topic: Aerodynamics vs. mass distribution  (Read 282 times)

Jeremy McCreary

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Aerodynamics vs. mass distribution
« on: July 17, 2017, 01:45:05 AM »

Nerd alert!

Ran into some interesting spin time trade-offs between aerodynamics and mass distribution with this new LEGO top...



The top consists of the black chassis below with or without fairings. The chassis has a central hub (not well seen) surrounded by a polyhedral space frame. The hub and frame were designed to cover the other's structural weaknesses. Together they're strong enough to hold the top's size and shape against torsion and centrifugal expansion to at least 2,000 RPM.



The frame's idealized geometry is that of a truncated octahedron with 24 identical vertices, 36 identical edges, and 14 faces of 2 different kinds (6 square and 8 hexagonal). The small black clamps mark the vertices. The square faces are embedded within the octagonal parts seen above. The hexagonal faces are empty.



Case 1. The very dirty bare chassis (above) turns in predictably miserable spin times: 7 sec by hand, and 9 sec with the starter in the Case 3 photo.

Reducing total aerodynamic braking torque (ABT) by fairing the chassis improves spin times significantly. However, the accompanying changes in mass distribution (especially AMI, AMI/TMI ratio, and CM height) also impact the results -- mainly via critical speed and the top's ability to resist any ABT present.

Case 2. With the addition of 48 mm lateral fairings (white below), spin times more than doubled to 16 and 24 sec, resp. Relative to Case 1, these fairings reduced total ABT and increased both AMI and AMI/TMI with little change in CM height. The happy result: Slower spin decay and lower critical speed.





So, any further spin-time gains to be had by adding axial fairings to the lateral fairings above? Well, that depends on the fairing size used!

Case 3: With 48 mm axial fairings, spin times actually dropped by ~20% (to 13 and 20 sec) relative to Case 2. Though AMI increased relative to Case 2, I suspect a net increase in critical speed due to a 10-15% increase in CM height and a reduction in AMI/TMI. How much these 48 mm axial fairings actually reduced total ABT relative to Case 2 is hard to say. (I can imagine a lot of interference drag at the triangular openings between fairings here.)



Case 4. The best spin times by far (30 and 51 sec!) came with the orange 64 mm axial fairings below (not in video). Relative to Case 2, adding these larger axial fairings reduced total ABT and increased AMI. Relative to Case 3, the decrease in AMI/TMI was less, and CM height was the same. Such a large boost in spin time probably required improvements in both ABT and critical speed.



Of course, release speeds (1,100 to 1,800 RPM) varied with spin-up method and from case to case. But my tests indicate that their contributions to the spin-time variations observed with a particular method weren't decisive.
« Last Edit: July 17, 2017, 02:28:43 AM by Jeremy McCreary »
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Playing with the physical world through LEGO

ta0

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Re: Aerodynamics vs. mass distribution
« Reply #1 on: July 17, 2017, 10:37:13 AM »

Just for its symmetry, I like your truncated octahedron top.  :)

My gut feeling is that the improvement with the side fairings is mostly due to the larger moment of inertial. It's not clear to me that aerodynamics would improve substantially.

My guess is that the main difference between 2, 3 and 4 have to do to the details of the air flow and therefore drag.

Perhaps you could compare the spinning drags by attaching them to a drill using a torsion spring and comparing the torque they produce at high speed (with flash photography)  :-\
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Iacopo

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Re: Aerodynamics vs. mass distribution
« Reply #2 on: July 19, 2017, 03:35:30 PM »

Case 4. The best spin times by far (30 and 51 sec!)

It's a much longer spin time, even if the top apparently isn't very much different from that of case 3.
Have you tried to repeat the spin, to check if the difference is real ?
At times tops spin for a longer or a shorter time without any apparent reason.  I think this is related to the contact points, with friction changing a bit because of wear of the contact points, or the top spinning on a different spot of the base, or maybe even some difference in lubrication.
When I make spin time comparisons with my tops, I have made a habit to calculate an average of more spin times, because the single spin time can be misleading. 
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Jeremy McCreary

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Re: Aerodynamics vs. mass distribution
« Reply #3 on: July 19, 2017, 09:03:58 PM »

Iacopo:  Yes, the spin time trends I reported are quite reproducible.

ta0: I have to think that aerodynamics figured significantly in the Case 4 result. In my experience with nearly 1,000 LEGO tops now, drag is usually the main  limit on spin times.

That's not to say that mass properties don't count. They do -- especially CM height and AMI/TMI ratio. It's just hard to make the kind of progress seen here without reducing drag in some substantial way.
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Iacopo

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Re: Aerodynamics vs. mass distribution
« Reply #4 on: August 23, 2017, 01:55:52 PM »

Perhaps you could compare the spinning drags by attaching them to a drill using a torsion spring and comparing the torque they produce at high speed (with flash photography)  :-\

You inspired me an experiment for air drag.  Not very accurate but decent enough.
I made a video about it:




Jeremy, after the experiment I see more clearly how spin time in your tops is lowered mainly by air drag, by far, and not tip friction.
« Last Edit: August 23, 2017, 02:02:43 PM by Iacopo »
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Jeremy McCreary

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Re: Aerodynamics vs. mass distribution
« Reply #5 on: August 24, 2017, 03:59:28 AM »

I like where you're going with this video, Iacopo! Funny, when ta0 came to visit last week, we discussed this very method of comparing total braking torques (TBTs) over breakfast. Great minds think alike.

Looks like you used a DC motor in your experiments, and that's good, because DC motor characteristics allow the following analysis...

Nerd alert!

Suppose you have a DC motor with no-load shaft speed N0 measured in RPM. Now let this motor spin up 2 different tops we'll call "1" and "2" until their speeds plateau at N1 and N2, respectively. Then the ratio of the TBTs Q1 and Q2 responsible for these plateaus is just

Q1 / Q2 = (N0 - N1) / (N0 - N2)

With a suitable test rig and a laser tachometer, it shouldn't be hard to measure speeds N0, N1, and N2 fairly accurately.

For example, if N0 = 1,000 RPM, N1 = 600 RPM, and N2 = 800 RPM, then Q1 / Q2 = 2. In other words, Top 1 generates twice the total braking torque at speed N1 as Top 2 does at speed N2.

Now, what we'd really like to know is how the TBTs compare when both tops are spinning at the same speed. Unfortunately, we won't be able to quantify that, but we can say at least this much: In the example above, Top 1's TBT would have to be greater than Top 2's if both were spinning at the faster slower plateau speed -- here, N2 N1. Otherwise, Top 1 2 couldn't have continued to slow the motor accelerate from there.

To get absolute values for Q1 and Q2 at the respective plateau speeds N1 and N2, we'd also need to know the motor's stalled torque Qs. Then for Top i,

Qi = Qs (N0 - Ni) / N0 = s (N0 - Ni),

where s == Qs / N0 is known as the motor's "steepness". When you play with lots of different DC motors as I do, steepness becomes a very handy thing to know.
« Last Edit: August 24, 2017, 11:43:02 AM by Jeremy McCreary »
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Jeremy McCreary

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Re: Aerodynamics vs. mass distribution
« Reply #6 on: August 24, 2017, 02:33:44 PM »

Watched your video again, Iacopo -- really well done. I would have expected the tape to cut the metal top's spin time, but not by that much!

Translating my last post to your experiments and terminology...

The motor speed with just the tape is not quite N0 but close, as the tape creates its own small aerodynamic load on the motor shaft at speed.

The RPM loss due to Flywheel 1 (say, squared rotor edge, no tape) is L1 == N0 - N1

The RPM loss due to Flywheel 2 (say, rounded edge, no tape) is L2 == N0 - N2

The fact that L1 exceeds L2 by an amount hard to attribute to experimental error alone allows you to say with confidence that at the lower plateau speed N1, Flywheel 2 generates less total braking torque than Flywheel 1.

And since you performed that experiment with the same 2 flywheels at 3 different voltages, you now say that about 3 different N1 values -- namely, 2116, 3310, and 3893 RPM.
« Last Edit: August 24, 2017, 03:14:37 PM by Jeremy McCreary »
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Iacopo

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Re: Aerodynamics vs. mass distribution
« Reply #7 on: August 25, 2017, 02:58:26 AM »

For example, if N0 = 1,000 RPM, N1 = 600 RPM, and N2 = 800 RPM, then Q1 / Q2 = 2. In other words, Top 1 generates twice the total braking torque at speed N1 as Top 2 does at speed N2.

This relationship is interesting.
Unfortunately I don't know the motor's stalled torque, so we are stuck with calculations.

The metal top's spin time was cut by the tape especially at high speed;
with the tape, it slowed down from 1750 rpm to 850 rpm in only one minute, so it lost more than 50 % of its speed in that lapse.  At that speed I can hear the noise of the air on the tape.

I believe your tops would spin much longer in a vacuum chamber.
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ta0

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Re: Aerodynamics vs. mass distribution
« Reply #8 on: August 25, 2017, 11:03:53 AM »

Great experiment Iacopo! Somebody had to do it and you took the initiative!  8)
Great idea Jeremy on using those relationships. Another possibility might be to measure the current of the motor required to keep it at a certain fixed speed, but I don't have time now to look into the details (there will be some change in the losses of the motor).
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Iacopo

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Re: Aerodynamics vs. mass distribution
« Reply #9 on: August 25, 2017, 12:21:41 PM »

Thank you, Ta0.  If calculations become simpler, it could be interesting.  Even if I am not sure how to change gradually the voltage, I have a transformer with only three outputs, 3, 5 and 6 volts.
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