Total dihedral formula for RES?

[fly1milehi]

Do any of you have a formula to determine the total amount of dihedral needed for proper roll and yaw on an RES design?

Just guessing, or by eye, or copying some other design is not good enough this time.

thanks
Greg

[Ollie]

From Dr. Drela:
"Ch = (A_hori/A_wing) * (tail_arm/avg_wing_chord)
Cv = (A_vert/A_wing) * (tail_arm/avg_wing_span )

"A well-sized tail will be in the range...
Ch = 0.35 - 0.50
Cv = 0.02 - 0.035
If the Ch and/or Cv are below the minimum values, the handling will suffer.



"My guess is that the majority of poly gliders out there
are spirally unstable to varying degrees. One easy way
to check is to set up a slow circle and then hold the
stick absolutely still and see what happens.

"The standard way to describe the severity of any instability
is the "time to double" Td. This is the time needed
for any initial disturbance to naturally double in magnitude
without any control input. This time varies inversely
with how far away the glider is from the neutral stability
point. If we define "Blaine's quotient" as

B = EDA x (tail_length/span) / CL

then the degree of spiral instability is given by 5-B, and Td
will be inversely proportional to 5-B (smaller Td = more unstable).

"For those who'd like to calculate it for their favorite
spirally-unstable glider, a reasonable estimate for Td
in shallow bank angles is:

Td = V / (60 g Cv) x EDA / (5 - B) (seconds)

V = flight speed in ft/s
g = gravitational acceleration = 32 ft/s^2
Cv = vertical tail coefficient = (tail_area/wing_area) x (tail_length/span)
EDA = equivalent dihedral angle in degrees

Say you have a 3m RES ship with marginal spiral instability:

V = 24 ft/s
Cv = 0.025
EDA = 10 deg

Here is Td versus a range of B:

B Td
---- -------
5.0 infinity
4.9 50 s
4.8 25 s
4.7 17 s
4.6 13 s
4.5 10 s
.
.

"Say your unstable glider has B = 4.5, and hence Td = 10 seconds.
You set up a steady 30 deg bank circle, and then hold the stick fixed.
Now a puff adds 1 degree of additional bank. The spiral will proceed
with this disturbance doubling every Td period as follows:

0 sec 31 deg ( 1 deg disturbance)
10 sec 32 deg ( 2 deg disturbance)
20 sec 34 deg ( 4 deg disturbance)
30 sec 38 deg ( 8 deg disturbance)
40 sec 46 deg (16 deg disturbance)
.
.

"This spiral grows very slowly, and can be easily quashed
by a nudge of rudder or aileron. Now let's say you have
a VERY spirally unstable glider with Td = 1 seconds.
The spiral will now proceed as

0 sec 31 deg ( 1 deg disturbance)
1 sec 32 deg ( 2 deg disturbance)
2 sec 34 deg ( 4 deg disturbance)
3 sec 38 deg ( 8 deg disturbance)
4 sec 46 deg (16 deg disturbance)
.
.

"The pilot better be quick, and paying very close attention
to the bank attitude to avert disaster. Thermalling this
glider will be very unpleasant and work-intensive.

"The point is that slight spiral instability can be dealt with
OK by the pilot, provided Td is sufficiently long. But on the
other hand if the glider is spirally stable, then the initial
bank disturbance will decay rather than grow, and the pilot doesn't
even have to bother correcting it. This self-correcting behavior
gives tactical benefits. You can freeze the stick and safely take
your eyes off the glider to skan the sky for signs of lift, or
just keep circling in your thermal when it drifts across the sun.

"One final thing to point out is that the vertical tail area
DOES matter when the glider is already spirally unstable.
If you double the tail area then you will double Cv, which will
halve Td. The glider will now spirally diverge twice as fast.
So a more precise restatement of my earlier claim is:

1) Increasing vertical tail area will not cause a spirally-stable
glider to become unstable.

2) If the glider is already spirally unstable, increasing vertical
tail area will proportionally increase the spiral divergence rate.

[CloudyIFR]

Ollie has it right, but if you don't like math, well other than basic measuring with a ruler in inches try my MS Excel spreadsheet for free!

It's called "Sailplane Calc".

The file is here:
http://h1.ripway.com/cloudyifr/files.htm

Help is here:
suterc@msn.com

Curtis
Montana

[Ollie]

Dr. Drela is right. I'm just his "student."

[mhodgson]

Back in the days when all this calculation stuff was for the bofins I was given a simple rule.
For each foot (30cm) of span put 1 inch (25mm) under each wing tip.
So a 6 foot span glider would have 6 inches under each tip.

Very simple, very basic and very mathematically inaccurate but you know what- it always worked.

[dharban]

Try this. I think it came from Charles River site.

Don Harban

[dharban]

That didn't work. Try this site:

http://www.charlesriverrc.org/articles/design/eda1.xls

[fly1milehi]

Awesome information everyone!! Thank you!

Greg

[histarter]

Back in the days when all this calculation stuff was for the bofins I was given a simple rule.
For each foot (30cm) of span put 1 inch (25mm) under each wing tip.
So a 6 foot span glider would have 6 inches under each tip.

Very simple, very basic and very mathematically inaccurate but you know what- it always worked.
Spiral stability

Olly does a fantastic job of interpolating Dr. Drela, however his approach just gets a snitch of the 2 blackboards full of math that the subject matter entails. Seriously, I prefer simplicity because I am only concerned with a narrow velocity range to handle thermalling at 6 to 9 mtr/sec. So, your 1 in 12" span is good enough for me - because it fits right into that velocity!:

Spiral stability is a FF term for consistant flight in a circle. If the machine tends to wonder out of a spiral, its circle diameter is increasing and this is called a under stable situation; whereas if the circular flight decreases in diameter until a spiral dive occurs, this is called over stabilized. A spirally stable aircraft will maintain its spiral when rudder trim is set for a diameter, and the aircraft goes round and round steadily. [Note: Under-stabilized was the Chicago Modelnuts favorite FF tuning. In a downer the spiral definitely opened to seek new lift; whereas, in lift the spiral stability improved, giving the FF a bit of selective hunting ability.

My approach to RC is a bit different. I tend to enjoy a bit of over stable bias because I find that with the different air flows generated by thermals, that a good thermal will attempt to tug my machine into a death spiral unless opposite rudder is used to hold off the “force”. This gives me an ability to sense the vertical speed of the thermal to core it efficiently. Obviously, the Time Constants have to be realistic so there is limits to prevent overage of the effect.

[fly1milehi]

You know I wish I could follow what your saying histarter. I dont understand how "over stable" means that you use less opposite rudder.
In my flying experience, when a glider enters a thermal "off center" the wing in the lift rises and forces the glider to turn away from the thermal and so it requires rudder to enter the thermal. When a glider enters a thermal "dead center" the whole plane rises, tail goes up, speed increases and the rudder input requires serveral adjustment to get the glider centered in the thermal..... Now depending on the size fo the thermal I have experience the following.... Getting tossed out of the thermal- which requires steady 'same rudder' (left rudder for a left hand circle) inputs to stay in the middle......... Getting "swallowed up" by a huge thermal which tends to make the glider "over bank" and yes that can result in a need for 'opposite rudder' (right rudder in a left hand circle).......... AND getting the "perfect" thermal where I can pretty much stay within the strongest lift with little to no rudder inputs. So Im not sure how Spiral Stability works there because its a fixed number built into the design of the plane's dihedral, tail moments, tail type, CG etc.

Maybe someone can shed more "technical light" on all of this. I do know that once the rudder, or rudder and ailerons have rolled and yawed any plane into a "steady rate" turn they return to their neutral postions and the rate of the turn pretty much continues on with only the elevator remaining deflected (and it remains at that setting for the rate of turn). So if a plane is spirally "UNstable" does it try to fall in the the center of the turn and try to tip stall? If a plane is spirally STABLE does it always try to return to straight and level flight?

ah.. the power of fluid dynamics!!!

[histarter]

You know I wish I could follow what your saying histarter. I dont understand how "over stable" means that you use less opposite rudder.
In my flying experience, when a glider enters a thermal "off center" the wing in the lift rises and forces the glider to turn away from the thermal and so it requires rudder to enter the thermal. When a glider enters a thermal "dead center" the whole plane rises, tail goes up, speed increases and the rudder input requires serveral adjustment to get the glider centered in the thermal..... Now depending on the size fo the thermal I have experience the following.... Getting tossed out of the thermal- which requires steady 'same rudder' (left rudder for a left hand circle) inputs to stay in the middle......... Getting "swallowed up" by a huge thermal which tends to make the glider "over bank" and yes that can result in a need for 'opposite rudder' (right rudder in a left hand circle).......... AND getting the "perfect" thermal where I can pretty much stay within the strongest lift with little to no rudder inputs. So Im not sure how Spiral Stability works there because its a fixed number built into the design of the plane's dihedral, tail moments, tail type, CG etc.

Maybe someone can shed more "technical light" on all of this. I do know that once the rudder, or rudder and ailerons have rolled and yawed any plane into a "steady rate" turn they return to their neutral postions and the rate of the turn pretty much continues on with only the elevator remaining deflected (and it remains at that setting for the rate of turn). So if a plane is spirally "UNstable" does it try to fall in the the center of the turn and try to tip stall? If a plane is spirally STABLE does it always try to return to straight and level flight?

ah.. the power of fluid dynamics!!!
Spiral stability is primarily for FF, or flying with your xmtr sitting on the ground (no pilot input) while your sailplane flys in a circle. In lift, machine speeds up somewhat but the circle stays the same; whereas in sink the machine slows down and the circle stays the same. If the sailplane cannot maintain the circle to begin with because of any upsetting disturbance makes it wonder off, it is under stable. Whereas any upset making the model tend to tighten the spiral for an eventual spiral dive, is an over stable state.