ALUMINUM ALLOYS AND HG TUBING

1. Aluminum and aluminum alloys
2. Typical aluminum tubes for HG
3. Maximun bending moment
4. Aluminum tubing sizes

1. Aluminum and aluminum alloys

Tubes of typical hang gliders are made of aluminum alloys 6061-T6 and 7075-T6 (zicral) alloy types.

Aluminum alloys http://en.wikipedia.org/wiki/Aluminium_alloy
Aluminum 7075-T6 http://en.wikipedia.org/wiki/7075_aluminium_alloy
Aluminum 6061-T6 http://en.wikipedia.org/wiki/6061_aluminium_alloy

Aluminum 7075-T6
is also known for trade marks Perunal, Zicral, Ergal, Fortal Constructal.

Mechanical properties of tubes used in HG:

 Name-source Code Ultimate strenght (2) Yield strenght (3) Elongation Density Modulus of elasticity kp/mm2 Mpa Mpa g/cm3 MPa Perunal (1) 7075-T6 53-64 2,81 Avional 100 (1) 2017A 38-55 Anticorodal (1) 6081-T6 32-36 Extradural (1) 6061-T6 25-28 k Wiki 7075-0 276 145 9-10% Wiki 7075-T6 510-538 434-476 5-8% Wiki 7075-T651 462-538 372-462 3-9% Wiki 6061-0 125 55 25-30% 2,70 Wiki 6061-T6 290 241 10% 2,70 Mathweb 7075-T6 524 462 11% 2,81 71,7 Mathweb 6061-T6 310 276 12% 2,70 68,9 Aluminum (pure) Al 7-11 2,70 70
Table 1: Mechanical properties of HG aluminum alloy tubing.

(1) Data from Finsterwalder tubing

(2) The maximum stress a material can withstand when subjected to tension, compression or shearing. It is the maximum stress on the stress-strain curve. Note: 1kp/mm2 is aprox 10 MPa.
(3) Below the yield strength all deformation is recoverable, and the material will return to its initial shape when the load is removed. This recoverable deformation is known as elastic deformation. For stresses above the yield point the deformation is not recoverable, and the material will not return to its initial shape.

Note also that the mechanical properties of 7075 depends geratly on the temper of the materials (ultimate strenght varies from 276 to 530 Mpa in temper "0" and temper "T6".

Another important detail is that the aluminum alloy 7075 has higher density (2.81 g/cm3) that the pure aluminum (2.70 g/cm3) and other alloys, due to the alloy with zinc, manganese and copper). However, their ultimate strenght, allows small tube thickness and therefore lighter than tubes of other alloys.

2. Typical aluminum tubes for HG

Typical diameters:

Crossbar: 60 mm
Leading edge: 52 to 48 mm (tubing 0,9 mm thickness)
Keel: 45 mm
Battens: 9 mm (3/8 x 0.035)
Triangle and king post: 25 mm x 1.6 mm thickness

Early standard hang gliders  had fewer tubing diameters.

LE SPS tubes

1-5/8" x 0,058    (41,28 x 1,47)   LE/Keel
1-1/2" x 0.058   (38,1 x 1,47)    LE/Keel
1" x 0,065   (25,4 x 1,65)    Antenna
3/4" x 0,065   (19,05 x 1,65)    Triangle

WW Falcon 3 tubes

Leading edge: 50x0.9 and 52x0.9 mm
Keel: 42x0.9 mm
Crossbar: 62x0.9 mm and 60x0.9 mm

WW Harrier (1981)

Leading edges 2" x 0.049 and 1.75" x 0.049
Keel 1.75" x 0.058
Xbar   1.75" x 0.049 + inner sleeve 1.625" x 0.035
Control bar leg 1.125" x 0.058 + inner sleeve 1.035"
Control bar base 1.125" x0.058

WW Raven (1979)

Leading edge 1.75" x 0.049 (44.45 x 1.24)
Keel 1.5" x 0.049 (38.1 x 1.24)
Xbar 1.75" x 0.049 (44.45 x 1.24)
Control bar 1.125"

La Mouette Sphinx
(...)

La Mouette Atlas

Seedwings Sensor 1 (1975)

Aluminum 6061-T6 1-3/4" x 0.049

3. Maximun bending moment

Why so many differences in the diameters of the tubes?
Depends on several factors:

a) Method of calculation
c) Size of the structure and types of joints between tubes
d) Geometry of the tubes (outer diameter, thickness)
e) Alloy type and temper
f)  Commercial availability

This section will analyze the influencing of factors d) and e)

Hang gliding tubes are under efforts of tensile, compression, bending, torsion and shear. The most significant efforts are bending and compression. The compression is greatest in the cross bar, and having to avoid the phenomenon of lateral buckling. The lateral buckling is avoided, also, by bending resistant sections. Then, the most important feature of the tubes of a delta is its resistance to bending.

Below is analyzed by the classical theory of strength of materials, and the theory of elasticity, maximum stress and maximum bending moment in a tube of outer diameter "D" and inner diameter "d".

Fig 1: Maximun bending moment in tubes

The conclusion is that the maximum moment resisted is:

Mmax= k x E x sigma_max

where:

k = geometrical factor defined by Laboratori d'envol as k = pi x (D4 -d4)/(32 x D)
E = modulus of elasticity of the material (aluminum alloys is 70 Mpa aprox)
sigma_max = maximum stress in the material, at the criteria of the designer, and probably less than the yield strenght (55 Mpa to 462 Mpa)

The geometric K-factor, is of the utmost importance, since it allows to compare the flexural capacity of tubes of various diameters and wall thicknesses.

The final choice of the tube is made by multiplying the factor k by the stress and modulus of elasticity of the alloy used. Previously, the maximal efforts in the estructure must have calculated (topic for another article).

Below, K-factor, calculated for tubes used in HG:

Table 2: K-factor and geometric properties of HG tubing. Also, in openoffice format: k-factor.ods

4. Aluminum tubing sizes

Commercial tubing sizes: (non metric units: 1inch=25,4 mm 1 lbs=453,6g 1ft=30,48cm)

 Ext diameter x wall (inch) Int diameter (inch) lbs per ft lbs unit ft unit 3/16 X 0.035 0.118 0.020 0.24 12 3/16 X 0.049 0.090 0.026 0.31 12 3/16 X 0.058 0.072 0.277 0.33 12 1/4 X 0.035 0.180 0.028 0.33 12 1/4 X 0.049 0.152 0.036 0.44 12 1/4 X 0.058 0.134 0.041 0.49 12 5/16 X 0.035 0.243 0.036 0.43 12 5/16 X 0.049 0.215 0.047 0.57 12 5/16 X 0.058 0.197 0.054 0.65 12 3/8 X 0.035 0.305 0.044 0.53 12 3/8 X 0.049 0.277 0.059 0.71 12 3/8 X 0.058 0.259 0.068 0.82 12 3/8 X 0.065 0.245 0.074 0.89 12 7/16 X 0.035 0.368 0.052 0.62 12 7/16 X 0.049 0.340 0.070 0.84 12 7/16 X 0.065 0.308 0.089 1.07 12 1/2 X 0.028 0.444 0.049 0.59 12 1/2 X 0.035 0.430 0.060 0.72 12 1/2 X 0.049 0.402 0.082 0.98 12 1/2 X 0.058 0.384 0.095 1.14 12 1/2 X 0.065 0.370 0.104 1.25 12 1/2 X 0.083 0.334 0.128 1.54 12 5/8 X 0.035 0.555 0.076 0.91 12 5/8 X 0.049 0.527 0.104 1.25 12 5/8 X 0.058 0.509 0.121 1.45 12 5/8 X 0.065 0.495 0.134 1.61 12 3/4 X 0.035 0.680 0.092 1.10 12 3/4 X 0.049 0.652 0.127 1.52 12 3/4 X 0.058 0.634 0.148 1.78 12 3/4 X 0.065 0.620 0.164 1.97 12 3/4 X 0.083 0.584 0.205 2.46 12 3/4 X 0.125 0.500 0.289 3.47 12 7/8 X 0.035 0.805 0.109 1.31 12 7/8 X 0.049 0.777 0.150 1.80 12 7/8 X 0.058 0.759 0.175 2.10 12 7/8 X 0.065 0.745 0.199 2.33 12 7/8 X 0.083 0.709 0.243 2.92 12 1 X 0.035 0.930 0.125 1.50 12 1 X 0.049 0.902 0.172 2.06 12 1 X 0.058 0.884 0.202 2.42 12 1 X 0.065 0.870 0.225 2.70 12 1 X 0.083 0.834 0.281 3.37 12 1 X 0.125 0.750 0.404 4.85 24 1 X 0.188 0.625 0.564 13.54 24 1 X 0.250 0.500 0.708 16.99 24 1-1/8 X 0.035 1.055 0.141 1.69 12 1-1/8 X 0.058 1.009 0.229 2.75 12 1-1/8 X 0.065 0.995 0.255 3.06 12 1-1/4 X 0.035 1.180 0.157 1.88 12 1-1/4 X 0.049 1.152 0.217 2.60 12 1-1/4 X 0.058 1.134 0.255 3.06 12 1-1/4 X 0.065 1.120 0.285 3.42 12 1-1/4 X 0.065 1.120 0.285 3.42 12 1-1/4 X 0.083 1.084 0.358 4.30 12 1-1/4 X 0.125 1.000 0.520 12.48 24 1-1/4 X 0.250 0.750 0.924 22.20 24 1-3/8 X 0.035 1.305 0.173 2.08 12 1-3/8 X 0.049 1.277 0.240 2.88 12 1-3/8 X 0.058 1.259 0.282 3.38 12 1-1/2 X 0.035 1.430 0.189 2.27 12 1-1/2 X 0.049 1.402 0.263 3.16 12 1-1/2 X 0.058 1.384 0.309 3.71 12 1-1/2 X 0.065 1.370 0.345 4.14 12 1-1/2 X 0.065 1.370 0.345 4.14 12 1-1/2 X 0.083 1.334 0.435 5.22 12 1-1/2 X 0.125 1.250 0.630 7.56 12 1-1/2 X 0.125 1.250 0.630 15.12 24 1-1/2 X 0.188 1.124 0.911 21.86 24 1-1/2 X 0.250 1.000 1.150 27.60 24 1-1/2 X 0.375 0.750 1.599 38.78 24 1-5/8 X 0.035 1.555 0.206 2.47 12 1-5/8 X 0.049 1.527 0.285 3.42 12 1-5/8 X 0.058 1.509 0.336 4.03 12 1-3/4 X 0.035 1.680 0.222 2.66 12 1-3/4 X 0.049 1.652 0.308 3.70 12 1-3/4 X 0.065 1.620 0.405 4.86 12 1-3/4 X 0.083 1.584 0.510 6.12 12 1-3/4 X 0.125 1.500 0.750 9.00 24 1-3/4 X 0.250 1.250 1.385 33.24 24 1-3/4 X 0.375 1.000 1.905 45.72 24 1-7/8 X 0.058 1.759 0.389 4.67 12 2 X 0.035 1.930 0.254 3.05 12 2 X 0.049 1.902 0.353 4.24 12 2 X 0.058 1.884 0.416 4.99 12 2 X 0.065 1.870 0.465 5.58 12 2 X 0.065 1.870 0.465 5.58 12 2 X 0.083 1.834 0.590 7.08 12 2 X 0.125 1.750 0.870 10.44 12 2 X 0.125 1.750 0.870 20.88 24 2 X 0.188 1.625 1.259 30.20 24 2 X 0.250 1.500 1.620 38.88 24 2 X 0.375 1.250 2.250 54.00 24 2 X 0.500 1.000 2.804 68.22 24 2-1/4 X 0.049 2.152 0.398 4.78 12 2-1/4 X 0.065 2.120 0.520 6.24 12 2-1/4 X 0.065 2.120 0.520 6.24 12 2-1/4 X 0.083 2.084 0.660 7.92 12 2-1/4 X 0.095 2.060 0.756 9.07 12 2-1/4 X 0.125 2.000 0.981 23.54 24 2-1/4 X 0.250 1.750 1.850 44.40 24 2-1/4 X 0.375 1.500 2.598 62.35 24 2-1/4 X 0.500 1.250 3.233 77.59 24 2-3/8 X 0.250 1.875 1.960 47.04 24 2-3/8 X 0.500 1.375 3.463 83.11 24 2-1/2 X 0.049 2.402 0.444 5.33 12 2-1/2 X 0.065 2.370 0.580 6.96 12 2-1/2 X 0.065 2.370 0.580 6.96 12 2-1/2 X 0.083 2.334 0.740 8.88 12 2-1/2 X 0.125 2.250 1.100 26.40 24 2-1/2 X 0.250 2.000 2.080 49.92 24 2-1/2 X 0.375 1.750 2.940 70.56 24 2-1/2 X 0.500 1.500 3.700 88.80 24 2-1/2 X 0.750 1.000 4.860 116.64 24 2-3/4 X 0.125 2.500 1.210 29.04 24 2-3/4 X 0.250 2.250 2.310 55.44 24 2-3/4 X 0.500 1.750 4.160 99.84 24 3 X 0.049 2.902 0.530 6.36 12 3 X 0.065 2.870 0.700 8.40 12 3 X 0.065 2.870 0.701 8.42 12 3 X 0.083 2.834 0.890 10.68 12 3 X 0.125 2.750 1.330 15.96 12 3 X 0.125 2.750 1.330 31.92 24 3 X 0.188 2.625 1.953 46.87 24 3 X 0.250 2.500 2.540 60.96 24 3 X 0.375 2.250 3.640 87.36 24 3 X 0.500 2.000 4.620 110.88 24 3 X 0.625 1.750 5.480 131.52 24 3 X 0.750 1.500 6.240 149.76 24 3 X 1.000 1.000 7.389 177.34 24
Table 3: Tubing sizes