General design approach
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General design approach |
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General design
approach – the Erik Dahl Christensen way How
do you use my method of
approach? You
have to settle on a wingspan, a minimum flying speed, a root chord and
an airfoil with a known critical Reynolds number. Remember
that the Reynolds number is calculated via the formula:
Re-number
= 70.000 x V x C
V
is the guestimated flying speed
C
is the wing chord in meters – this means that the wing has different Reynolds
numbers at different places along the wingspan. 1)
First
you settle on a minimum flying speed. This is the minimum flying speed
where you want the wing to be efficient, and not flying below the
critical Reynolds number. According
to Martin Hepperles/Stefan Siemens ”tip-theory” this gives you the
wing chord at 90% of the wingspan. 2)
Next
you settle on a root chord. 3)
These
2 numbers together with the wingspan is what you need to calculate the
modified elliptical wing form: The
root chord I call C-root The tip-chord at 90% span I call C-90 Now comes the math
– keep your
tongue vertical and fasten your
seatbelts: Tau = (Ln (C-tip) – Ln (C-root) ) / (-0,83) This gives you a constant I call ”tau”
– Ln is the natural
logarithm – the sign on you calculator is ”ln” The next step has a lot to do with trigonometry: You have to determine the places where you want special chords; these
places are compared to half the span: Lets say that you have a wingspan of 3200mm and you want to know the
chord 1000mm from the fuselage. Half the span is 1600mm and 1000/1600 is
0,625. C-0,625 = (cosine(arc-sine (0,625)))tau x
C-root This way you can calculate your new wingform and calculate the wingarea. The
generally formula is: C-unknown = (cosine(arc-sine (unknown)))tau x
C-root 4)
Next
is some key numbers for a wing, which all interferes with each other: a)
Aspect
ratio
= (span x span) / area b)
Area
= (span x span) / aspect ratio c)
Span
= square root ( span
x area) Next
you have to choose an airfoil and check the camber of it – since it is
hard to do by hand, I have made a short list of different airfoils
camber: Airfoil:
Camber Aquila
(common flat bottom) 5,0% SD
7032
3,7% Clark
Y
3,6% SA
7038
3,3% SD
7037
3,0% S
3021
3,0% HQW
3,0/9
3,0% SA
7036
2,8% SA
7035
2,6% HD
48
2,5% HQW
2,5/9
2,5% MH
32
2,4% HD
48b
2,3% HQW
2/8
2,0% RG
15
1,8% SD
7003
1,5% Consult
other homepages or sources for information on data from other airfoils. a
lot of airfoil printing software gives you theses data. Having
the airfoil, check the polar of it, and determine which is the highest
Cl-value that the airfoil can operate at (it may be between 0,9 and 1,2)
at the Reynolds numbers you are operating at. This will also help you to
determine the slowest speed you may fly at. It is very common that it is
possible to fly slower without a tip stall, but it is NOT efficient (it
may be with a ”common” flat bottom airfoil but I doubt that was the
airfoil you choose?). Flying slow means that you are flying at a high
Cl-value. The estimated Cl-value gives you a minimum flying weight,
which you should not go below: Weight
= (V / 1,278)2 x A x Cl V
is still the minimum airspeed A
is the wing area Cl
is the Lift coefficient -
Cl-value To
be on the safe side, I often calculate with the conservative Cl-value of
0,9. This gives me a calculated flying weight that is very realistic.
And remember that this weight is a minimum weight if you want to fly
with a not-critical Re-number at this Cl-value (lifting coefficient).
Most planes a very capable of flying slower and with at lower weight,
but they will not be efficient. 5)
Now
you can check if the airfoil you choose can do the job. Calculate the
wing loading, and check if you have chosen an airfoil that can roughly
fit this
table:
Camber:
Minimum wing loading:[1]
4,0%
15-18 g/sqdm
3,0%
21-27 g/sqdm
2,5%
30-33 g(sqdm
2,0%
33-36 g/sqdm
1,5%
36-39 g/sqdm This is where you might be surprised. First of all most gliders are flying far to slow to be efficient. This means that if flown a tad faster, they would have e better glide angle without having a worse sinking speed. Secondly most gliders are way to LIGHT! WHAT? Erik has finally lost his grip - too light? Yes, medium- to heavyweight gliders penetrates better – with, across and against the wind! How many times do you have a contest or just a normal flying day in no-wind conditions?? Why build a glider for those 3 weekends every second year?? And third, the normal glider-guiding guy uses airfoils with way too much camber (on a light glider). Remember that the Reynolds numbers depend on the flying speed, and when you use a less cambered airfoil on a more heavy glider, the airspeed rises – and so does the Reynolds number and this causes the airfoil drag to decrease. This way you end up with a glider that’s flying faster but sinking at approximately the same speed. Voila – you now have a glider that stays up just as long as your first glider, but it covers twice as much ground (and thermal filled air). All you have to do is to get used to the little faster flying speed that may be the hardest part. Dave Thornburg: said: "We have lift to burn" - and he said it many summers ago when he wrote about his Bird of Time in Model Airplane News.
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