Minimum airspeed for RC Plane

[James McGill]

Hi All,

I'm working on replacing my motor and propeller, but I'm unsure how to
work out what the minimum speed required for the plane to stay
airborne is. The motor + prop I'm looking at give a thrust:weight
ratio of 0.8, and a pitch speed of 56km/h. Searching tells me that the
thrust:weight ratio is probably spot on for a trainer, but I've got no
idea how to tell if that pitch speed is too slow or too fast. Any
ideas?

Regards,
James

[Iain Chalmers]

To a first approximation, it's al about the wing loading - weight divided by wing area.[1]

An old "rule of thumb" in RC circles is that stall speed in mph is approximately 4 times the squareroot of the windloading in ounces per square foot. 

So a light weight glider might be around 4oz/sqft and it'd stall at ~ 8mph.

A typical powered RC trainer is around 16oz/sqft, and it'll stall somewhere round 24mph (~38kmh)

How much do you expect your plane to weigh with the new motor/controller/battery, and what's it's wing area?

I'd bet that so long as your wingloading is under 16oz/sqft, it'll fly OK.

(And apologies for the archaic units of measure, but that's how all the largely us-centric forums still discuss things… And it does make that "four times the squareroot of the wing loading" thing easy…)

big

[1] airfoil, aspect ratio, wing planform, and probably a bunch of other stuff too - all affect stall speed as well, but wing loading is the big determinant, especially down in model plane sizes where the difference between a flat sheet of foam and a thousandths-of-an-inch-accurate cnc milled airfoil are surprisingly smaller than most people would guess. 

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[Dr Ada Not-a-fruit]

I'm going to go into a bit of theory here, because the idea of a
minimum speed or 'stall speed', although attractive and useful as a
first approximation, doesn't tell the whole story.

Classically, there are four forces (or sets of forces) on a plane
which is flying, which we will call thrust, lift, drag, and weight.
I'll use a world frame of reference here, so weight points straight
down. For an aircraft to remain at a constant altitude, lift==weight.

Weight = mg
Lift = 1/2 C_l rho A V^2

rho is constant(ish), A is constant, and C_l is (roughly) 2*pi*alpha,
where alpha is the angle of attack. The critical angle of attack
(where you get the most lift) is roughly pi/12, so C_l at the critical
angle of attack is roughly 5/3, and we'll assume it's summer and rho
is 1.2. Substituting this all in:

mg = 1/2 C_l(crit) rho A V^2
= 5/6 rho A V^2
V^2 = 1.2 mg / rho / A = mg/A

which leads to Iain's wing loading result. (if you want, we can
convert it to decimal and make it 110 km/h *sqrt wing loading in kg
per sq decimeter).

However, this is not the end of the tale. Model aircraft are
astoundingly powerful for their size - your model has the same thrust
to weight ratio as a loaded F-35 on afterburners. Depending on what
angle you mount your engine at, the prop's thrust can contribute to
lifting force. for example: if you mount your engine at 15 degrees
to the wings, then at 15 degrees angle of attack, you'll have half of
your thrust contributing to lift. That means that we can change the
above equation to

V^2 = mg/A - 1/2 mg * thrust-weight ratio
= 0.6 mg/A (in this case with TWR = 0.8)
or roughly 80km/hr *sq rt wing loading

However, this doesn't work perfectly because as you approach the pitch
speed of your plane, the available thrust goes down.

If your thrust to weight ratio is above 1, then everything goes out
the window because you don't need your wings to fly anymore.

On Jul 9, 12:38 pm, Iain Chalmers <bigi...@mightymedia.com.au> wrote:
> [1] airfoil, aspect ratio, wing planform, and probably a bunch of other
> stuff too - all affect stall speed as well, but wing loading is the big
> determinant, especially down in model plane sizes where the difference
> between a flat sheet of foam and a thousandths-of-an-inch-accurate cnc
> milled airfoil are surprisingly smaller than most people would guess.

Your critical angle of attack and available lift are essentially the
same no matter what shape your wings are. What airfoil, aspect ratio,
planform etc do affect are:
- most critically, induced drag (and thus lift-drag ratio)
- what happens at the stall

wings stall progressively; there's no such thing as stall speed for a
wing. as you go past the stalling angle of attack (roughly 17 degrees
as we said earlier) some of the airflow detaches from the wing and you
get progressively less lift as you increase angle of attack, but it
doesn't go to zero immediately.

[Iain Chalmers]

On Wed, Nov 7, 2012 at 12:07 AM, Cosmin Cojocaru <cjcr...@gmail.com> wrote:
> Hello. I am building an indoor double propeller uav. My thrust to weight
> ratio is about 1.7 ( One propeller has a 7 Newton thrust and my plane is 900
> grams which is 7.84N). My wing loading is 4.5 kg/m2 . What stall speed do
> you think I will have?

A 4.5kg/m2 wing will stall at around 23kmh or 6.5m/s. (see previous
discussion in this thread).

If you want to slow the stall speed down, your only options are to
reduce weight or increase wing area (or both). If you doubled your
wing area, you'd drop the wing loading to 2.25kg/m2 and get a stall
speed down around 16kmh or 4.5m/s.

Having said that, you've got enough power-to-weight there to "prop
hang", so stall speed might not be as much of a concern as it would
seem. Although the wing would stop holding the uav up below stall
speed, if you've got suitable stability control it'd stay in the air
at zero forward speed.

> My purpose is to get a very small stall speed because
> the uav is supposed to fly indoor at low speeds. Any suggests for
> improvements?

Work out whether you want to build "half a quadcopter with vestigial
wings", in which case the major problems are going to be stability
control and battery capacity; or if you really want a "plane that
flies mostly using it's wings", where you'll have to determine a
reasonable flying speed (your ~6.5m/s speed would be _way_ too fast
for loungeroom flying, it might be OK if by indoors you mean a large
hall or basketball court), then work out you absolute minimum weight
for your powertrain/controlsystem/payload, and calculate the required
wing area to achieve your target flight speed.

My guess is you'll find to fly a ~900g uav slow enough to use in a
loungeroom - you'll need a wing bigger than the loungeroom can fit. I
wouldn't want to try flying anything much faster than 2m/s in my
loungeroom, which at 900g requires just over 2 square meters of wing
area. (Hmmm, maybe a 1.5mspan x 450mm chord triplane? Then build two
of them, for indoor dogfighting…)

big

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