discspeed wrote: I don't know much about angular momentum, but I suspect the weight distribution does something to the spin(holds rpms longer?) on the disc, which can also affect how it flies considerably.
Well... that's actually precisely what angular momentum means in regards to a disc.
Yes, that's right. I've been over this before (sigh)...here goes again:
Consider the disc to be composed of 2 pieces: the rim (approximately a thin cylinder), and the flight plate (approximately a flat disc). The rim has mass M_r, and the flight plate has mass M_fp. The outer radius of the flight plate (where it meets the inside of the rim) is R_fp, and the average radius of the rim is R_r.
The moment of inertia of the disc (assuming a flat flight plate) is the sum of the flight plate and rim (formulas for thin cylinders and flat disk shapes are well-known):
I = I_fp + I_r = M_fp*R_fp*R_fp/2 + M_r*R_r*R_r
The total mass is:
M = M_fp + M_r
Notice that a heavier disc has a greater moment of inertia, it goes in proportion to total mass, regardless of how it is distributed. A 175g disc has 17% greater moment of inertia than a 150g disc, with everything else being the same.
Usually R_r is just a little bit larger than R_fp, and we can approximate R_r~R_fp=R. Then the moment of inertia is much simpler:
I ~ (M_fp/2+M_r)*R*R
If all the mass is in the flight plate, then:
I ~ M*R*R/2
If all the mass is in the rim, then:
I ~ M*R*R
So there you have mathematical proof that the most you can change the moment of inertia of a disc is by a factor of 2, corresponding to all mass in the flight plate vs all mass in the rim. (Actually, even this isn't achievable unless you can find a strong weightless plastic for the flight plate, which doesn't exist.)
Let's compare the Wizard and Ion (from PDGA specs):
Gateway Disc Sports Wizard 174.3g/21.0cm/2.1cm/1.8cm/19.0cm/1.0cm/8.6/59.25/10.43
MVP Disc Sports Ion 174.3g/21.0cm/1.9cm/1.6cm/18.8cm/1.1cm/7.6/62.50/2.83
The Wizard rim is a tad deeper, while the Ion rim is a tad thicker...these are similar in magnitude and probably trade-off fairly equally in terms of volume. However, with the Wizard being a thicker profile (2.1 cm vs 1.9 cm), it is going to be a slower disc than the Ion...the aerodynamic differences might be too great to allow for valid comparison between moment of inertia effects alone, but we'll try it anyways.
The Wizard moment of inertia (using avg of inner and outer rim radius for R_r) is:
I_wiz = 0.0045125*M_fp + 0.01*M_r (units of kg*m^2)
For the Ion:
I_ion = 0.004418*M_fp + 0.00990025*M_r (units of kg*m^2)
Notice that the coefficients are just about the same (they only differ by a couple percent...not surprising, since their dimensions are very similar). We can write the moment of inertia for both molds approximately as:
I_both = 0.0045*M_fp + 0.01*M_r (units of kg*m^2)
This makes it simple, and the error involved is only ~1%.
Let's assume max weight, 0.1743kg(=M=M_fp+M_r). Then we can write (I'll show all the steps, for clarity):
I_both = 0.0045*M_fp + 0.01*(M-M_fp) (units of kg*m^2)
I_both = 0.0045*M_fp + 0.01*(0.1743-M_fp) (units of kg*m^2)
I_both = 0.001743-0.0055*M_fp (units of kg*m^2)
Written in this way, the real limitation on moment of inertia is the mass of the flight plate. If you can lighten the flight plate, while putting more mass in the rim (which requires increasing the density of the rim plastic), then you can increase the moment of inertia. This is pretty much what we've already talked about, but I've put some actual numbers in it.
So, here is the essential question regarding Wizard vs Ion moment of inertia: how much lighter is the Ion flight plate (mass M_fp_ion) than the Wizard flight plate (M_fp_wiz)? The relative difference in moment of inertia between the 2 discs is just:
(I_ion-I_wiz)/I_wiz=(M_fp_wiz-M_fp_ion)/(0.317-M_fp_wiz) ...(using kg for mass, instead of g)
(I_ion-I_wiz)/I_wiz=(M_fp_wiz-M_fp_ion)/(317-M_fp_wiz) ...(using g for mass, as we're used to doing)
Would you hazard a guess as to the mass of the Wizard flight plate? Let's just say it is 1/2 the disc mass (which is 87g at max weight), just for the sake of demonstration. Then we would have:
(I_ion-I_wiz)/I_wiz=(87-M_fp_ion)/230 ...(still using g for mass units here)
If the Wizard flight plate were half the mass of the disc, and MVP managed to lighten their flight plate by a factor of 2 in the Ion relative to the Wizard (this is being quite generous!), then the difference in moment of inertia between the Ion and Wizard would be about 19%. This change, if valid (recall I'm just throwing rough numbers out for the mass of the flight plate), would then be similar to the moment of inertia difference between a 150g and 175 g disc, all else being the exact same. However, you can't compare the flight effects of the moment of inertia for a light and heavy disc the same way you'd compare 2 discs with the same total mass, since the lighter disc ascends and descends at steeper angles than a heavier disc just owing to a smaller mass alone, and this also figures into the stability (since this changes the angle of attack)...so be careful not to take this analogy and run with it.
So, there you have my best guess-timate for the change in moment of inertia of MVP's "gyro" technology discs relative to standard single plastic discs. Playing with different numbers, I would guess that it likely falls in the range 10-20% gain in moment of inertia. This isn't a huge difference, so the next question is whether this amount of change in moment of inertia will have a significant impact on flight for discs of exactly the same weight. I'll save that for the next post (after I get other stuff done).