Envelope Demo – preparations

So we are now trying to build envelope coming with shape around something like this:

As you may see it is quite simple concept of joining two ellipsoids with interlaced cylinder reaching maximum diameter of 2m. So the front part is traditional ellipsoid with w=2.5 (A), followed by a central cylinder w=1 (B), closed by another ellipsoid of w=3 (C). The plan is to buckle in the ellipsoid A so it will all end up being ~6m long.

The idea is to do a 5:1 scaled model and send it to Windreiter guys for review and a quote. To be able to do so, we actually need to draw parts which we can glue together next. Here we’ll be using classical pie/rugby-ball seems method, hoping that it will all work out when inflated.

Having a radius of 1m, maximum circumference comes to 6.28.

C=2πr=2·π·1≈6.28319

Divided by 6 to get height of each part we are getting h=1m. Scaling down 5:1 this is 20cm + 2cm for seem we have the first parameter 22cm.

With the W – part A this is going to be half-ellipse of -> 52cm (scaled 2.5m/5 + 2cm for seems), part B is a simple cylinder of 20cm and part C is -> 62cm (scaled 3m/5 + 2cm for seems).

To get this transformed this onto a paper, I prepared myself a tiny Excell helper (with another help from here). Where X is calculated with =B$2*COS(RADIANS($A5)) and Y =B$1*SIN(RADIANS($A5)).

Ellipse A:

H	22.00
W	52.00
a	x	y
0	52.00	0.00
10	51.21	3.82
20	48.86	7.52
30	45.03	11.00
40	39.83	14.14
50	33.42	16.85
60	26.00	19.05
70	17.79	20.67
80	9.03	21.67
90	0.00	22.00
100	-9.03	21.67
110	-17.79	20.67
120	-26.00	19.05
130	-33.42	16.85
140	-39.83	14.14
150	-45.03	11.00
160	-48.86	7.52
170	-51.21	3.82
180	-52.00	0.00
190	-51.21	-3.82
200	-48.86	-7.52
210	-45.03	-11.00
220	-39.83	-14.14
230	-33.42	-16.85
240	-26.00	-19.05
250	-17.79	-20.67
260	-9.03	-21.67
270	0.00	-22.00
280	9.03	-21.67
290	17.79	-20.67
300	26.00	-19.05
310	33.42	-16.85
320	39.83	-14.14
330	45.03	-11.00
340	48.86	-7.52
350	51.21	-3.82
360	52.00	0.00

Ellipse B:

H	22.00
W	62.00
a	x	y
0	62.00	0.00
10	61.06	3.82
20	58.26	7.52
30	53.69	11.00
40	47.49	14.14
50	39.85	16.85
60	31.00	19.05
70	21.21	20.67
80	10.77	21.67
90	0.00	22.00
100	-10.77	21.67
110	-21.21	20.67
120	-31.00	19.05
130	-39.85	16.85
140	-47.49	14.14
150	-53.69	11.00
160	-58.26	7.52
170	-61.06	3.82
180	-62.00	0.00
190	-61.06	-3.82
200	-58.26	-7.52
210	-53.69	-11.00
220	-47.49	-14.14
230	-39.85	-16.85
240	-31.00	-19.05
250	-21.21	-20.67
260	-10.77	-21.67
270	0.00	-22.00
280	10.77	-21.67
290	21.21	-20.67
300	31.00	-19.05
310	39.85	-16.85
320	47.49	-14.14
330	53.69	-11.00
340	58.26	-7.52
350	61.06	-3.82
360	62.00	0.00

Of course we’ll use just a part of those ellipses getting:

And:

Now let’s get practical!