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Thermal, Structural, and Inflation Modeling of an Isotensoid ...

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!<br />

where<br />

<strong><strong>an</strong>d</strong><br />

!<br />

N<br />

!" = b<br />

P ref<br />

#R 2 ,<br />

f f<br />

= "f r<br />

(31)<br />

#<br />

" =1+<br />

1 $ % 2 (32)<br />

" = 1# f r<br />

# T r<br />

(33)<br />

Note that γ is strictly greater th<strong>an</strong> one, so the front fabric<br />

stress <strong><strong>an</strong>d</strong> meridi<strong>an</strong> tension will be greater th<strong>an</strong> the rear<br />

values. Equations ! (30) <strong><strong>an</strong>d</strong> (31) show that the peak stresses<br />

occur when the value <strong>of</strong> internal pressure is the highest. It<br />

was shown in the inflation <strong>an</strong>alysis section <strong>of</strong> this paper that<br />

the internal pressure is directly proportional to the<br />

freestream dynamic pressure, so we c<strong>an</strong> fairly assume that<br />

the peak stresses will occur at the full pressure time, t fp . The<br />

burble fence load, N b , at time t f is computed using modified<br />

Newtoni<strong>an</strong> flow theory for a half-torus as 80.8 kN.<br />

Predicted meridional cord loads <strong><strong>an</strong>d</strong> fabric stresses for the<br />

three minimum gauge materials considered are shown in<br />

Table 5. The safety factor is the ratio <strong>of</strong> the material tension<br />

strength to the computed fabric stress. For the meridi<strong>an</strong>s, a<br />

cord diameter <strong>of</strong> 1 cm is assumed for the safety factor<br />

calculation. These results indicate that minimum gauge<br />

materials are more th<strong>an</strong> capable <strong>of</strong> h<strong><strong>an</strong>d</strong>ling the maximum<br />

fabric stresses in the isotensoid. Additionally, meridional<br />

cords c<strong>an</strong> be constructed <strong>of</strong> the same material as the<br />

envelope fabric with plenty <strong>of</strong> margin from failure. Thus,<br />

the material sizing shown in Table 3 is assumed in<br />

subsequent thermal <strong>an</strong>alyses.<br />

Table 5 – Maximum fabric stresses <strong><strong>an</strong>d</strong> safety factors for<br />

c<strong><strong>an</strong>d</strong>idate SIAD materials. Cord safety factor assumes a<br />

1 cm diameter meridi<strong>an</strong>.<br />

Tensile<br />

Strength<br />

(MPa)<br />

Cord<br />

Load<br />

(N)<br />

Cord<br />

Safety<br />

Factor<br />

Fabric<br />

Stress<br />

(MPa)<br />

Fabric<br />

Safety<br />

Factor<br />

Material<br />

Nomex 600 5972 8 13 46<br />

Kevlar 3600 5972 47 21 174<br />

Vectr<strong>an</strong> 3000 5972 39 21 145<br />

<strong>Thermal</strong> Analysis<br />

<strong>Structural</strong> <strong>an</strong>alysis shows that minimum gauge materials c<strong>an</strong><br />

perform suitably, so the temperature history <strong>of</strong> the c<strong>an</strong>opy<br />

c<strong>an</strong> now be computed using the thermal model discussed<br />

earlier. It is <strong>of</strong> primary interest to deduce whether or not the<br />

fabric temperature will exceed the thermal capability <strong>of</strong> the<br />

stressed materials. Also <strong>of</strong> interest is the sensitivity <strong>of</strong> the<br />

temperature results to different thicknesses <strong>of</strong> elastomeric<br />

12<br />

coating. Underst<strong><strong>an</strong>d</strong>ing this relationship informs parametric<br />

SIAD mass models requiring coating thickness as <strong>an</strong> input.<br />

The maximum temperature in the fabric as a function <strong>of</strong><br />

thermal coating density is shown in Table 6. Note that<br />

adding a modest amount <strong>of</strong> coating c<strong>an</strong> greatly reduce peak<br />

temperatures. This addition adds thermal mass, ρc p , to the<br />

material stack <strong><strong>an</strong>d</strong> effectively raises the amount <strong>of</strong> energy<br />

required to increase the fabric temperature.<br />

To better visualize the effect <strong>of</strong> increasing the coating<br />

thickness, the Vectr<strong>an</strong> fabric temperature histories for three<br />

coating thicknesses is shown in Figure 16. It is evident that<br />

adding additional coating both reduces the peak temperature<br />

<strong><strong>an</strong>d</strong> slows the process <strong>of</strong> temperature ch<strong>an</strong>ge.<br />

Temperature, K<br />

Table 6 – Maximum fabric temperatures for different<br />

Viton coating thicknesses.<br />

<strong>Thermal</strong> Coating Areal<br />

Density (ozm/yd 2 )<br />

450<br />

400<br />

350<br />

Fabric Temperatures (K)<br />

Nomex Kevlar Vectr<strong>an</strong><br />

1 489 435 446<br />

3 444 411 418<br />

6 407 387 391<br />

1 ozm/yd 2<br />

3 ozm/yd 2<br />

6 ozm/yd 2<br />

300<br />

0 5 10 15 20 25 30<br />

Time, s<br />

Figure 16 – Vectr<strong>an</strong> temperature histories for different<br />

amounts <strong>of</strong> Viton outer coating.<br />

The thermal mass effect c<strong>an</strong> also be seen by comparing the<br />

temperature histories <strong>of</strong> the three materials for a fixed fabric<br />

thickness, as shown in Figure 17. Kevlar has approximately<br />

16% higher ρc p th<strong>an</strong> Vectr<strong>an</strong>, <strong><strong>an</strong>d</strong> Nomex has<br />

approximately 68% lower ρc p th<strong>an</strong> Vectr<strong>an</strong>. A sensitivity<br />

<strong>an</strong>alysis showed that the peak temperature difference c<strong>an</strong> be<br />

almost entirely attributed to thermal mass differences. That<br />

is, Kevlar’s relatively low thermal conductivity does not<br />

influence the peak temperature results relative to the higher<br />

thermal conductivity materials. The thickness <strong>of</strong> the SIAD<br />

envelope is so low that even a large difference in thermal

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