AeroModeller – June 2018

fl uid mechanics, similarity; it never ends.

Truly Ruly

So now I am going to tell it like it is. Read

this before you ever open a text book

on aerodynamics. If Newton creeps in

here somewhere, forgive me, I am only

supercool, while Newton is ultra-supercool!

We start at low speed: so low we aren't

moving. Later we are going to go faster,

much faster, really fast - hypersonic!

I was standing in my driveway when

a something fell onto my fore-arm. The

“something” was a tiny seed with a fuzzy

hairdo, like a parachute but with no

aerodynamic lift at all, just a lot of drag. As

the seed fell, so air tried to navigate its way

through the hairs. But air has a property

of “stickiness”, also called viscosity. I

suppose another word for sticky might be

“viscid”, as the textbooks call air “inviscid”

when they want to ignore the stickiness.

The point here is that the seed would fall

slowly, then be carried by the wind to a

destination remote from its birthplace.

Reynolds Number

The buzz word here is “Reynolds number”.

The “number” has a value, formed from

the product of speed and length. For this

seed, the number might have been zero,

so the “Reynolds number” was in fact

zero. All small, slow fl ying things have low

Reynolds numbers. They could go faster,

but then their air resistance makes that

hard for them.

Here is a rule of “thumb”. For wings with

operational Reynolds numbers less than

150,000, drag is high and getting worse

as the Reynolds number falls. Above

150,000, you can start to neglect the drag,

it is still considerable but not disastrously

so. Except in model airplanes! Reynolds

numbers then are like 60,000; they are

bad, you must take great care with the

shape of the wing cross-section: thin and

high cambered sections might be the way

to go.

But some classes of model require

high speed AND low speed performance.

Say slow while circling in a thermal, then

speeding up to go between thermals. Then

you need the publication “Airfoils at Low

Speed”, Soartech 8, by Selig, Donovan

and Fraser, 1989, published by H. A.

“Herb” Stokely. These are sections wind

tunnel tested for Reynolds numbers from

60,000 to 300,000.

Now we don't have any picture of air yet.

Air is a vast number of molecules all racing

around, crashing into each other. Their

speeds are very high, on average about

450 m/s: jet fi ghter speeds! Imagine a

swarm of bees, where the bees can crash

into each other (collide). While the swarm

is not moving along, the internal motion

of the swarm is referred to as “thermal”.

That is, the motion of the molecules is

the source of the term “temperature”.

There are two other properties of the

swarm, “pressure“, and “density”. By

some cunning trickery in a subject called

“thermodynamics”, the properties of

temperature, pressure and density

are linked.

Mach number

The next trick is to imagine that you have

upset the swarm of bees, so that they are

chasing you. If you can run at say 200

m/s, with the bees still in pursuit, then the

properties of temperature, pressure and

density in the swarm are little changed.

The buzz word then is “incompressible”.

With “incompressible” fl ow, we can ignore

the thermal, random, collision motion of

the air within the swarm.

But now something very fundamental

changes. As the speed of the swarm

increases toward the speed of the motions

internal to the swarm, the air starts to

be compressed. To repeat, as we go

from a swarm of 200m/s and faster, with

internal molecular speed 450m/s, then

compression occurs to a measurable

extent. Now the speed of sound is about

330m/s, depending a on air temperature.

So now we have the internal speed in

the swarm, the speed of the swarm itself

and the speed of sound all of comparable

magnitude. Now the wheels fall off. We can

ignore the buzz word “Reynolds number”,

in favour of a new one. This is the “Mach

number”. Simply divide the speed of

the swarm by the speed of sound in the

48 AeroModeller - June 2018

Aerodynamics, Books & More!

FAR LEFT: Something slower, no

dynamics at all! 9 mm long seed

dispersal unit is all viscosity, near

zero Reynolds number. Just like a

balloon with zero-buoyancy, the

right term is aero-static device.

Fell out of the sky onto my arm;

could have come from anywhere

of similar latitude in the world.

LEFT: These seeds of known

origin, collected from the weeds

in my back “garden”. Don’t knock

this low-Reynolds number trick.

We have “Bogong” moths here in

Oz, which each year travel from

Southern Queensland to the high

country of Northern Victoria,

some 1600 km: so many that they

block up the air-conditioner inlets

in Parliament House, Canberra.

ARMCHAIR PART 29.indd 48 26/04/2018 14:31