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--- ideas:super-pressure_balloon_skin_tension_calculations [2018/06/14 21:40] – created rocketboy
+++ ideas:super-pressure_balloon_skin_tension_calculations [2018/06/21 12:38] (current) – rocketboy
@@ Line 1: / Line 1: @@
 ====== Super-pressure skin tension estimation ======
-On this page we estimate the tension in the skin of a super-pressure balloon.  We will make a number of identified assumptions as we go along.
+On this page we estimate the tension in the skin of a super-pressure balloon.  We will make a number of identified assumptions along the way.
 In order to estimate the surface tension we must first calculate the pressure differential between the inner and outer surfaces of the balloon.
@@ Line 7: / Line 7: @@
 The outer pressure is simply the local atmospheric pressure at the height the balloon is floating.  The inner pressure is determined by the volume of the balloon, the mass of gas contained, and its temperature.
-For the balloon and its payload to be floating the balloon must be displacing the same weight of air as that of the balloon and payload.  We can calculate the volume of air being displaced (and hence that of the balloon) by knowing the local air density.
+For the balloon to be floating at a constant altitude the balloon must be displacing the same weight of air as that of the balloon (including gas) plus payload.  We can calculate the volume of air being displaced (and hence that of the balloon) by knowing the local air density.
 The local atmospheric pressure, density and temperature can be determined from an atmospheric model.
-The Skin tension can then be calculated with the standard skin tension equation
+If we assume a spherical balloon the skin tension can then be calculated with the standard sphere skin tension equation T = Pd . r / 4
+Where Pd is the differential pressure (inside to out) and r is the sphere radius.
 Here is an example:
 Kg balloon + 7Kg fabric envelope
 Kg payload
-cu m of Helium at launch - assume STP  (Standard Temperature & Pressure)
+m^3 of Helium at launch - assume STP  (Standard Temperature & Pressure)
 	Floating at 25,000m/82,000ft
+m^3 of helium provides enough lift for the balloon + fabric envelope and payload and additional lift for a reasonable ascent rate.
 Using the the 1962 NASA standard model at an altitude of 25,000m:
@@ Line 28: / Line 32: @@
 We have a total of 13.327kg to lift (3kg Latex balloon, 7kg fabric, 1kg payload, 2.327kg of helium)
-So floating at 25,000m we must displace 13.327kg of air – since the local air density is 0.03995 kg/m^3 we will be displacing 333.6 m^3 of air.
+So floating at 25,000m the balloon must displace 13.327kg of air – since the local air density is 0.03995 kg/m^3 the balloon will be displacing 333.6 m^3 of air.
-Assume a sphere shape for the balloon balloon - volume V = (4/3) . Pi . R^3
+Assume a sphere shape for the balloon balloon - volume V = (4/3) . Pi() . r^3
 which gives an r of 4.3m – diameter 8.6m
@@ Line 44: / Line 48: @@
 External Pressure Po =  2.48277kPa
-Differential pressure Pd (Pi - Po) = 3.135kPa – 2.48277kPa = 0.6522kPa (about 0.08psi) very similar to observed latex balloon flights.
+Differential pressure Pd (Pi - Po) = 3.135kPa – 2.48277kPa = 0.6522kPa (about 0.08psi - very similar to observed latex balloon flights).
 Surface Tension of a spherical container is given by T = (Pi – Po). r / 4
-Surface tension units are force/length – so the units come out right (since kPa = kN/m^2)
 	T = 0.6522kN/m^2 . 4.3m / 4 = 0.701115 kN/m
-.1N/m = 71.5kgf/m = 157.6lbf/m = 48lb/ft
+.1N/m = 71.5kgf/m = 48lb/ft
-Some of that tension will be borne by the latex balloon, some by the fabric.
+This spreadsheet allows you to calculate the surface tension for a non-eleastic constraining envelope:
+{{:ideas:constrainedfloaterv1.xls|}}