Some math, for math people who like math. (and WMDs)
This is how the world ends this is how the world ends... pretty much exactly as expected.
@Enjou Adjustments to
@Radvic's plan.
Zephyr's reach bullets - Have keiko or Mari test this. They'll need to go to a wide open area, either way up in the air or slightly above the ocean. Use ZR on a 10 gram pebble and see how fast they can rotate it at the farthest part of their range, using mirrors for line of sight, if necessary. Actually, first try only the largest circle within the front of their range. If ZR has no maximum velocity limit, this should be near super sonic. If this works, spend time perfecting their aim and otherwise getting used to the new application of ZR. (also try this with a circular arrangement of wind wall, either deactivating it to fire or casting a second wind wall to divert the sped up bullet to it's desired path.
Zephyr's reach seal assisted bullets - Cut a paper into a circle and infuse a storage seal and 2 LBfs on it(make verticle lips as necessary for LBFs to work) on it. Store a small rock in it. Try using ZR to make it spin about it's center, flat side up, as quickly as possible, activating it by lowering a lip with ZR when it's fully up to speed. If this seems like a viable weapon, Mari and Keiko should practice with it before we leave our camp and we should make a reasonable amount of them.
Both ZR tests should be done behind appropriate defenses composed of 5BS and force walls.
Some complaints about these:
spinning paper disk
Spinning at fast speeds is different than spinning at high RPM. For a disk, the bursting speed of the material is dependent on the tensile strength and the material density (see: specific strength). From
Space tether - Wikipedia
"the material's "specific velocity" which is equal to the maximum tangential velocity a spinning hoop can attain without breaking"
is V = sqrt(Specific Strength)
Thus, we need specific strength of at least V^2. for 1300 m/s tip speed, this means 1690 e3 m^2/s^2.
See
Specific strength - Wikipedia for a table of typical Specific Strengths.
If you reduce the speed to say 720 m/s, youre at the specific strength of Balsa wood at 520 e3 m^2/s^2 (which despite low tensile strength has very low density).
You may still be satisfied at this speed...
However, you also face trouble with unsealing many things in approximately the same space. The things you unseal have volume, and you are trying to unseal them extremely rapidly... before you have any chance for the previous item to clear the area. Either seal failure or odd collision mechanics ensue. Some redesign of release mechanism is in order
Second:
Spinning in the open atmosphere, large radius:
Air drag is going to affect this, as you mentioned. Here's a way to calculate it-
mS = .01 kg (mass of stone from your math)
Rad = 50 m (radius from your math)
FZephyrMag = 44.5 (from your math)
rhoA = 1.225 kg/m^3 (density of air)
rhoS = 2650 kg/m^3 (density of stone - granite specifically)
Figure out the cross-sectional area of the pebble, assuming a sphere
VS = .01 / 2650 = 3.8 e-6 m^3 (Volume)
rS = (VS * 3 / (4* pi))^(1/3) = 9.7 e-3 m (radius)
AS = 3.0 e-4 (Area)
Drag Coefficient
CD ~ .8 (
Cannonball Aerodynamic Drag) for sphere close to Mach 1
You need to use vector summation to combine mutually perpendicular forces
FZephyrT = force due to zephyr reach that is not used to cancel gravity, or used in centripetal acceleration
FZephyrZ = gravity cancel force
FZephyrR = centripetal Force
FZephyr = [FZephyrR, FZephyrT, FZephyrZ] (R to center of circular motion, T tangent to circle, Z up and down)
= [mS*vel^2/Rad, .5*rhoA*vel^2*AS*CD, .1]
for simpler math, assume FZephyrZ ~ 0... i.e. vel^2 * [mS/Rad, .5*rhoA*AS*CD, 0]
FZephyrMag = vel^2 * sqrt( mS^2/Rad^2 + .25*rhoA^2*AS^2*CD^2) = vel^2 * B
where B = sqrt( mS^2/Rad^2 + .25*rhoA^2*AS^2*CD^2)
B = 2.5 e-4 for the numbers provided
vel = sqrt(FZephyrMag/B) = 426 m/s
once released, the sphere sees a drag force of
.5*rhoA*vel^2*AS*CD ~ 26.65 N which decelerates the sphere (initially) at 2665 m/s^2
once released, the sphere accelerates downward at 9.8 m/s^2
Assuming an initial altitude of 1.5 m (Keiko eye level?) and no initial vertical velocity, ground impact after .56 s (ish), at a velocity of ~93 m/s, range 102 m (hitting their feet)
Velocity/Range will be a bit higher, because CD is decreasing with Mach. impact speed will be no greater than 141 m/s, at a range of ~131 m, again impacting at foot level (done by setting CD to 0.45)
The spreadsheet isn't too hard to build in excel, so long as you don't mind cruddy first order Euler approximations for integration.
Bullet shapes and spinning the bullet will change this, but probably not by as much as you might think.
