How does the mechanical linkage of the ASI convert dynamic pressure into KIAS?
 

I understand the underlying principle of an ASI, ie. that it uses the Pitot-static system to measure the dynamic pressure as the difference between total pressure and static pressure.
Knowing that the dynamic pressure is proportional to the square of airspeed, any (linear) immediate variation in the measure of dynamic pressure will be a linear variation in the square of airspeed, not in airspeed alone. Yet the ASI markings are themselves uniformly spaced and still, they show airspeed, not airspeed squared.

Therefore: how does the mechanical linkage convert a linear variation (change) in the dynamic pressure into airspeed?

That is, how is the square root transformation of dynamic pressure performed at the clockwork level of the ASI to obtain the KIAS?

My guess is that one of the gearwheels will be responsible for this but I haven't actually been able to find any information on this online. Any help or insight would be greatly appreciated

I'll go out on a seriously precarious limb here and say (having looked at a picture of the innards of an ASI, sorry I can't reproduce it here easily), that:
1. Assuming that the centre of the capsule (which pushes a horizontal lever) extends with the square of the speed, then
2. That extension, which is turned into a rotational movement of a vertical rod, has less effect the further the capsule extends, because of the rotation of the vertical rod. That is, the first mm turns the vertical rod say 2 degrees; the next mm turns it 1 degree and so on (a bit like a piston in its travel - at top and bottom dead centre the crankshaft rotates heaps but the piston doesn't move much, whereas halfway between those two points the piston moves fast for a small rotation of the crankshaft.) It's a sine curve kind of thing.

Ready to be shot down any minute now!

Actually what Matty J said is probably more like it.

OK. Here is a guess.

How the needle moves depends on the compression of the round, flat cylinder within the ASI. At zero differential pressure, zero deflection. At x differential pressure, deflection is y. y=f(x).

There is no reason to assume the function f(x) is linear. Indeed it is more likely to be non-linear as the more compressed it is the more it's likely resist. This is the instrument maker's magic.

Certainly, without delving into the math of elastic deformation of metals, there must be a lot of trial and error design to come up with the shape of the anneriod diaphram within the ASI. The pitot does its bit by deriving and transmitting total pressure to the inside of the diaphram with static pressure fed to the outside internals resulting in a direct reading of dynamic pressure. Gears and cams can easily derive a mechanical answer to a complex equation.

Basic...diaphram expands with increase in total pressure against the static pressure within the instrument. This movement is linked to a shaft that also has a lever, which acts upon a sector...this is where the math is done. The shaft turns according to movement of diaphram, the lever on the shaft acts on the sector...as the sector moves it presents more movement as the lever slides along the side of the sector. The sector acts through a gear to turn the needle on the dial. There is also adjustment available through a spring that can be adjusted to give more or less resistance to the expanding diaphram.

No, they ain't uniformly spaced.

http://www.flight-mechanic.com/wp-co...016/06/7-7.gif

Pitot-Static Flight Instruments ? Airspeed Indicator (ASI)

Blimey, you're right. Actually, there are all sorts of markings, uniformly and non-uniformly spaced ones.
Here's a good example from a Piper Warrior that shows that the distribution of marking spacing is neither constant, nor a linear function of KIAS.
Because it is a nonlinear function of airspeed, this confirms that there's a transformation of the displacement taking place a the mechanical level.
This could indeed be done through calibration of the membrane expansion, or using a lever that actuates a gearwheel through a guide.

Apart from the aforementioned boffin magic.


ASI from 06:42