So after all of the calculations and design work I have started to build the initial 2 foot test structure.
I’m really anxious to see if this idea will even work. There’s a reason these kind of models aren’t that common. Trying to get a rigid frame structure, with the weight constraints and limited lift makes it quite a challenge.
You might have noticed that my work so far hasn’t been very precise. I haven’t been accounting for the width (1/8″ and 1/16″) of balsa wood beams in my designs up to now, and have been working primarily from a wire frame design.
There are so many variables to consider. Glue, bevel cuts in the wood, excess material along the seams of the gas bag. All of those things matter, but it would be a monumental task to do all of that math. So I am basically working on rough estimates here, and not exact numbers (even though I’ve used a lot of decimal places at times!).
So I will plug along here and build the test frame, then cover it, then make the gas bag, then weigh the whole thing, then fill the bag with helium.. And we will all see if it works and lifts the weight it is supposed to.
I could be on the right track, or it could fail miserably. Either way, it will all be posted here for you to see. If it fails at least we will hopefully learn something from it.
Back to the 2′ test section.. I wanted to get an idea of what the whole thing would weigh complete with the outer covering and gas bag installed prior to building. There may (probably will) also be some thread used to cross-brace each panel, but that shouldn’t add much to the overall weight.
Each of the 16 sides is 4 11/16″ long, so the total length all around the mid-section is 75″. Therefore the area, 75″ x 24″ (length), of the outer covering should be 12.5 ft2.
I will probably be using clear (so I can see the test structure) Top Flite MonoKote to cover the exterior. This material should weigh around 0.44232 g/ft2, so the outer covering of the 2′ long test section (12.5 ft2) should be about 5.529 grams total (0.195 oz).
The mylar foil material I will be using for the gas bags is sold by Balloon Kits, and a 1 lb (44″ x 16 yards) roll is $28.50 USD. So a 1 ft2 section of the material should weigh about 2.577 grams (or 0.00568 lb). And the diameter of the gas bag is 22.1875″ (1′ 10 3/16″).
C = π D
C = 3.1459 * 22.1875 = 69.7996″
So the circumference of the gas bag should be 5.8166′ (or 69.7996″). We will multiply this by the length of the gas bag (24″ / 2′), which should make the outer area of the gas bag 11.6332 ft2 (1,675.18 in2).
At 2.577 grams (0.00568 lb) per square foot the weight of the cylindrical part (around the body) of the gas bag should weigh around 29.978 grams (1.057 oz).
We already know from a previous post that the area of each circular end of the gas bag should be around 386.444 in2, so the total area of both ends should be 5.367 ft2 (772.888 in2), which should add another 13.83 grams (0.4878 oz).
So the total weight of our 2′ long gas bag for the test section should weight in around 43.808 grams (1.545 oz). This worries me a little, it’s heavier than I was thinking it would be. So I will be keeping an eye open for other potential gas bag materials.
We also know from a previous post that the balsa wood frame will weigh 52.395 grams (1.848 oz). So the total weight of our 2′ test section looks like it will weight around 96.203 grams (3.3935 oz). I think we’re still okay, since the section should be able to lift 152.2856 grams, but we need some left over lift for the nose and maybe the tail where there will be a much higher ratio of structure to lift.. and then there will be some electronics and servos. It will be close.
I was anxious to see what the airship would look like with tail fins, so I finally added some. And I am really pleased so far with the overall shape of the airship. She’s gonna look good.
My airship will have 17 rings total, and the tail fins will attach aft between the 15th and 17th rings. Once completed, the overall length of the airship will be 8′ 9″.
I have not yet settled on a design for the control surfaces on the fins just yet though. I’m still working on the design so the system will only use 2 small servos without interfering with gas bags. And I would like to have the weight of the servos, etc, more toward the center of the craft (where most of the lift is) if possible.
Once again I used the arc tool in Sketchup to make the nice curve on the front of the tail fins.
I have not yet bothered with things like the control gondola that will attach under the bow, probably between the 4th and 6th rings. No need to mess with that just yet.
Before I start building the nose and tail I will post more detailed designs with all of the dimensions and some additional notes.
So I have been working on finishing the rest of the frame design in Sketchup. I added a nose on to a previous design I had going when I was still thinking of using carbon fiber rods for the frame, so the main body rings were spaced 12″ apart.
I have since decided to build with balsa sticks, since they’re lighter. But, they’re also not as rigid. So I have added four more main rings to the main body so that they are all spaced 6″ apart to add some rigidity to the design.
The nose is 1′ 9″ long, with 3 more smaller rings (1′ 10 1/2″, 1′ 5 11/16″ and 8 1/16″) spaced 6″ apart, with a 3″ long tip. I still haven’t figured out which size balsa sticks each smaller ring will be made from just yet, but should be deciding that soon.
The nose section turned out well, so I went on to add a tail to the frame. It will be 3′ long, with gradually smaller rings (1′ 11 3/8″, 1′ 9 9/16″, 1′ 6 7/16″, 1′ 2″ and 7 7/8″) spaced 6″ apart, with a 6″ long tip.
Next I will be adding 4 fins to the tail and posting that soon.
I was initially trying to decide on a diameter for my airship. At first I was working some math on both a 3′ diameter and a 2′ diameter. Then I remembered that I live in an apartment, and I will need to be able to fit this thing through a normal single door.. So 2 foot diameter it is!
To start I created a 2′ diameter ring, with 16 sides, using Sketchup. The program makes it easy to then draw a circle (arc) from the center out until it meets up with the inside of the rings, and then I can get the area of the circle too with a right-click menu choice. But this ended up wrong since it’s not measuring a circle, but a polygon.. So I used 1′ 10 1/4″ for the diameter (rounded up a bit).
Most folks that graduated high school learned how to calculate the volume of a cylinder. But if high school was a couple of decades ago there are online tools to do it for us! Basically, the area of the base x the height of the cylinder = volume. So..
Area = πr2
3.14159 x 11.1252 (11 1/8″ radius) = 388.8208 in3
..and we know that there are 144 (12 x 12) inches in a square foot, so..
388.8208 / 144 = 2.7001 in2
So we know that each 1 foot length of this cylinder has a volume of 2.7001 ft3, and our test section is 2 feet long, so the gas bag should have a volume of 5.4002 ft3.
Anyway.. Now we need to find out if this gas volume can lift the frame as we’ve designed it. So we will add up the weight of the construction materials (minus glue) to see if this design might actually work.
I may post some data on the calculations with carbon fiber rods later, but at this point I’m pretty sure I’ll be building the test section with balsa wood sticks. So for now we’ll focus on the weight of a balsa wood frame.
The outer part of the rings, and the longitudinal stringers, will use 1/8″ balsa sticks. And the inner bracing of the rings will use 1/16″ balsa sticks. I weighed a 36″ section of the 1/8 balsa and it weighed 2 grams. So a 36″ section of the 1/16″ should weigh 0.5 grams.
This 2′ test section of the frame will use 63′ 3″ of the 1/8″ balsa and 124′ 6″ of the 1/16″ balsa (probably a bit less, since I’m not accounting for bevel cuts). The weight of the 1/8″ sticks should be about 42.1667 grams, and the weight of the 1/16″ sticks should be about 10.2083 grams. So the total weight of the balsa wood frame should be around 52.395 grams.
We know that 1 cubic foot of helium can lift about 28.2 grams. So the 5.4002 ft3 our gas bag holds should be able to lift 152.2856 grams (about 5.4 ounces). So we’re doing well so far since the frame only weighs 52.396 grams! Stay tuned and we’ll factor in the weight of the exterior covering and the gas bag materials next.