MHD vortex experiment and theory

Here I give an explanation for the vortex that appears above a magnet when doing water electrolysis.

The basis is this video  https://www.youtube.com/watch?v=SAl1LVPbYhY  in which the author of the experiment claims the vortex is “unknown to science”.

I have successfully replicated the experiment and provided annotations that fully explain the phenomenon:

When applying voltage between 2 submerged electrodes, the water molecules split into hydrogen and oxygen molecules, with hydrogen also in the form of positive ions.

When a charged particle (hydrogen ion bubble) moves in a magnetic field, it will experience a perpendicular force according to Lorenz Law.

In this case, the magnetic field has a vertical axis of symmetry (the ball magnet sits vertically), with horizontal radial components that generate a vertical torque in the formation of rising bubbles which engage with the neutral surrounding water in a vortex.

Multicopter propulsion theory

I have worked a little on the physics of an electric multicopter (true for helicopters as well) to prove one of the ways to optimize for longer flight time.

Original post: http://www.rcgroups.com/forums/showthread.php?t=1733300#post22754326

Why the maximum flight time for a given frame is obtained with a battery of equal weight (=1/2 of total weight) ?

Firstly, for a propeller we have:
thrust F = kt * p * d^3 * w^2
input power P = kp * p * d^4 * w^3
where p, d – propeller pitch and diameter, kt and kp – specific constants and w – angular velocity.

Playing with the 2 formulas we get: F / P = kt * sqrt(kt) / kp * sqrt(p * d / F)

But we have a given frame(p, d – constant) therefore P = k * F * sqrt(F), where k is a constant that shows proportionality (from now on I’ll use k to show that, but it’ll not be the same k, meaning it will not have the same value), and its value doesn’t matter.

Note that we have worked out P as mechanical power, we need to find out P(el) – that is electrical power drained by motors from the battery.
Now I’m cheating a bit, and assume that P(el) is not propotional to P(mechanical output) for an electric motor, but with P * sqrt(F). Meaning that the more we “push” a motor, the lower its efficiency (I know it’s only half true). The term sqrt(F) might not seem to make much sense at this point, but we’ll see later on that it drastically simplifies the demonstration.

So we write:
P(el) = k * F * sqrt(F) * sqrt(F) = k * F^2

Then F must be equal to copter weight (hover), which is (m+M) * g. M is frame mass(constant), m is battery mass and g – gravitational acceleration.

Therefore:
P(el) = k * (m+M)^2

Now, battery energy is proportional to its mass, E = k * m

Flight time is t = E / P(el)

Substituting P(el) we get t = k * m / (m+M)^2

After playing with inequalities, we find out that the expression m / (m+M)^2 has a maximum value of 1 / (4*M) (remember that M is constant and m is variable), reached if and only if m=M. This means t is maximum when for the given frame, we choose a battery with m=M.

I don’t have enough batteries at the moment to experiment and check the validity of the theory, however I will attach a real data graph I found on the mikrokopter site, which seems to be in accordance.
The maximum flight time is achieved for 14 000mAh capacity which on 4s weighs around 1kg – very close to the empty frame weight (970g) :

Computer soundcard tachometer

Measure the angular speed of a propeller using an IR LED – Sensor, a soundcard and some windows software.
I have originally posted it on the forum: http://www.rcgroups.com/forums/showthread.php?t=1450032

TGY 9X transmitter telemetry hack

This is a simple hack to activate telemetry on the Turnigy 9x  RC transmitter. Someone came with this idea on a forum and I have applied it in a different configuration:  http://www.rcgroups.com/forums/showthread.php?t=1510047
Everything is explained in the video (make sure you have annotations on):

You will also need to to this cut on the other side of the board (I missed it from the video):