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A Fair CurveA fair curve is one which changes direction smoothly, without any kinks. A simple way to check whether a curve is 'fair', is to sight down the curve. That means you look along the curve just like a marksman would sight between the eyesight and foresight of a rifle. To do this you need to get down so your eye is almost in line with the surface of the paper and look down the curve. It also means you must move from side to side to see the whole curve, so sometimes it is more convenient to put the drawing with the curve on a flat board and hold it up to eye level and then turn the board so you can 'follow' the curve with your eye. Please note the use of the singular - sighting is always done with one eye.
Below is an example of a fair curve followed by an example of a curve with a slight 'kink'.
Try sighting along these curves and you will see the 'kink' in the second one far more clearly even though it is fairly obvious.
The importance of the 'fairness' of a curve is so lines generated mathematically to have a gradual curve, even though it may have increasing or decreasing curvature, a kink identifies a point that is incorrect. The fault can lie in the calculations or in the marking out of points. Regardless of which of these two is responsible for the fault, checking the fairness of the curve is often the last chance to correct any errors because very often, once a curve is marked out the next step is to cut the material or to set up some form of solid post along the curve for further construction of some kind.
Checking the fairness of the curve is a very important step! ! ! !
Cutting and joining Gores
Once a gore has been cut, it is either good or it is a reject. It is good if the error made during cutting left extra material on the 'off-cut' side. It is a reject if the cut has infringed 'into' the gore outline. If the 'infringement' is small the piece 'may' be recoverable depending on the method of joining you have chosen. Check the curve before cutting and again after cutting.
Cutting the full size gore requires care, patience and accuracy [assuming the marking out is accurate]. If you are going to cut multiple layers, make sure they are held down firmly so the blade of your knife does not move them relative to one another. If they move, your final product will not be what you wanted and if you are really unlucky, the surface will not be 'fair'. In other words, the difference will show up as a visible dent in the airform, which might mean a visible dent in the ceiling of your structure.
Assuming you are using some kind of tough plastic sheet for your airform, the common method of joining the gores would be to tape them together with butt joints using a suitable adhesive tape. To do this successfully, you will need a frame with the curvature of your ellipse to make the joint [typically made from ¾" thick board of some sort]. Because the gore material is light a shed is probably needed as even breezes could cause problems in handling the gores. The size of the shed depends on the size of your ellipse and obviously must accommodate the major half-axis [across the corners plus some walking space will do]. In order to reduce the height you need you can slice off a piece of the profile as shown in the sketch below. If you do that, you will need a slightly larger space because the distance between the corners of the profile is greater than the major half-axis.
You must pin the gores down one at a time along the profile making sure the edge of the first gore is perfectly straight. You can then pin the second gore next to it so the edges of the two gores touch but do not overlap. You can then add small strips of adhesive tape between the pins across the two gores followed by a long length of tape starting almost at one end of the joint removing pins as you go. You may need to cut this strip as you go, if you move off the joint line, and start again with some overlap.
Joining the gores at the center
The easy part of taping gores together is where they are nice and wide. The difficult part is where all the points come together. The way to 'sidestep' this problem is to replace the pointed end of the gores with a circle of gore material. To do this you must cut off all the pointed ends of all the gores at the identical length. You can do this as early as the marking out stage. A fair place to do it is where the gore is about twice as wide as the tape you are going to use. You then simply tape in a circle of gore material in the hole that is left in airform.
The diameter of the circle is the x-dimension at the station where you 'cut off' the 'points' of your gores. Although this piece of flat material is no longer the true shape, it will tend to bulge when you inflate the form so you will not be able to notice the flatness even though you know it is there.
The base
Assuming the inside of the dome is going to be a flat surface like a floor, the joint between the walls of the airform and the base is critical. That joint must be designed and made in a way it allows you to anchor it firmly to the ground when you inflate the airform otherwise it will lift off the ground as the base attempts to assume a spherical shape. Lightweight airforms require fairly low pressures. If you use 1" of water gauge inflation pressure there is a lift force of a little more than 5 lb per square foot of floor area trying to lift your airform off the ground. If your floor area is 1000 sq ft the force is more than 5000 lb/f.
Whatever your lift force, each 'ground attachment' need only hold its bit of the lift force. If you have 100 attachments each one only holds 1/100th of the lift force. Whatever you do, over design this part of your construction process.
Scale model
The gores are the building blocks of the airform, which in turn will determine the shape of the final product. The procedure of marking out the gores, cutting them and joining them is going to be a demanding task. I strongly recommend you build a scale model of your airform before you start on the real thing.
There is no better way to learn than by doing, but the cost could ruin you. Make a scale model!
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