Upscales and Downscales

Don't confuse these terms with 'scale' modeling, which is building a detailed version of a real rocket. Rather, 'scaling' a rocket design means building a larger or smaller version of the original, like a big Mosquito or miniature Big Bertha.

When scaling a model (or anything else), the first step is determining the scaling factor. We'll upscale an Estes Mosquito to demonstrate. The original BT-5 tube measures .544" in diameter, and the desired BT-60 tube measures 1.637" in diameter. Dividing 1.637 by .544 results in a scaling factor of 3.00 (rounded, use more decimal places and/or forget the rounding for more precision). In other words, a Mosquito built using a BT-60 body is three times larger than the original, or 300% bigger. Sometimes you’ll see this mentioned as a 3x upscale.

This scaling factor is what you will multiply every measurement by for the new model. So the original 3" length of BT-5 would become a 9" length of BT-60, and you would multiply each of the fin dimensions the same way for the upscaled version. There are two possible exceptions to this. One, you don’t always want to upscale the thickness of the fins, or that upscaled Mosquito will have fins 3/16" thick. It’s up to you. The second exception is nose cones. Unless you have a truly scaled version of the original nosecone, the length is probably wrong to some degree, or the shape is slightly (or not so slightly) different. What I do in these cases is to measure the length of the true upscaled nosecone, compare it to the length of the available nosecone, and then adjust the length of the body tube to make up the difference. For instance, if the upscaled nosecone should be 4" long, but the nosecone you have is only 3" long, my solution is to make the body tube 1" longer to compensate. Close enough is usually good enough.

To reverse the above, and downscale an Estes Big Bertha, we’ll take 1.637" (diameter of the original BT-60) and divide it by .544" (diameter of the desired BT-5), which gives a scaling factor of .33. So a BT-5 Big Bertha would be a 1/3 sized downscale, or 33% as large as the original. Just like above, all dimensions are multiplied by the scaling factor, which makes the original 18" long BT-60 a 6" long BT-5. Adjusting for fin stock thickness and nose cone/body tube lengths are done the same way as well.

Doing the measurements and calculations in metric (millimeters), makes things much easier.

That’s the theory and the math. Below is a table I keep handy by my workbench with measurements and scaling factors for many common sizes of tubing. To use the table, find the original size body tube down the left hand column, then find the desired size tubing along the top row. Cross index the column and row to read the scaling factor to use. The two columns farthest left on the table have the metric and standard diameter measurements for the body tubes. Adding other sizes to the table is easy to do by using the techniques above. Obvious additions are Apogee 10.5mm tubes and tubes for the Micro Maxx sized rockets.

One neat thing about the table is using it to help scale fin templates using a photocopier. The copier I have access to will make reductions/enlargements from 64% to 155% of the original size. Suppose I want to upscale an Estes Alpha to use BT-80 sized tubing. Looking at the table, this means the scaling factor is 2.72, or the fin template needs to be enlarged 272%. Looking at the table (and knowing the capabilities of my copier), I see I can enlarge the original fin template by 154%, making the template the correct size for a 1½" tube. Next, I take that new (enlarged) template and use it as the original, enlarging it again by 148%, for a BT-70 tube. Finally, I’ll enlarge this new template by 117%, giving me a fin pattern perfectly sized for the BT-80 tubing I’m going to use. It’s easier to do than to explain, so just follow it through using the table to see the steps.

Upscales and downscales are fun and interesting. The Mosquito is a classic that’s done often, and makes a good first project. After that, the possibilities are endless, just look through past issues of Sport Rocketry and High Power Rocketry for examples, and old catalogs for ideas.

std	met	...	BT-5	BT-20	BT-50	1.1"	BT-55	BT-56	1.5"	BT-60	2"	2.1"	BT-70	2.5"	BT-80	3"	4"	5.5"	6"	7.5"	11.4"
0.544	13.8	BT-5	...	1.36	1.80	2.04	2.44	2.48	2.79	3.01	3.72	3.90	4.12	4.64	4.76	5.57	7.43	10.22	11.14	13.93	21.18
0.544	13.8	BT-5	...	1.36	1.80	2.04	2.44	2.48	2.79	3.01	3.72	3.90	4.12	4.64	4.76	5.57	7.43	10.22	11.14	13.93	21.18
0.544	13.8	BT-5	...	1.36	1.80	2.04	2.44	2.48	2.79	3.01	3.72	3.90	4.12	4.64	4.76	5.57	7.43	10.22	11.14	13.93	21.18
0.544	13.8	BT-5	...	1.36	1.80	2.04	2.44	2.48	2.79	3.01	3.72	3.90	4.12	4.64	4.76	5.57	7.43	10.22	11.14	13.93	21.18
0.544	13.8	BT-5	...	1.36	1.80	2.04	2.44	2.48	2.79	3.01	3.72	3.90	4.12	4.64	4.76	5.57	7.43	10.22	11.14	13.93	21.18
0.544	13.8	BT-5	...	1.36	1.80	2.04	2.44	2.48	2.79	3.01	3.72	3.90	4.12	4.64	4.76	5.57	7.43	10.22	11.14	13.93	21.18
0.544	13.8	BT-5	...	1.36	1.80	2.04	2.44	2.48	2.79	3.01	3.72	3.90	4.12	4.64	4.76	5.57	7.43	10.22	11.14	13.93	21.18
0.544	13.8	BT-5	...	1.36	1.80	2.04	2.44	2.48	2.79	3.01	3.72	3.90	4.12	4.64	4.76	5.57	7.43	10.22	11.14	13.93	21.18
0.544	13.8	BT-5	...	1.36	1.80	2.04	2.44	2.48	2.79	3.01	3.72	3.90	4.12	4.64	4.76	5.57	7.43	10.22	11.14	13.93	21.18
0.544	13.8	BT-5	...	1.36	1.80	2.04	2.44	2.48	2.79	3.01	3.72	3.90	4.12	4.64	4.76	5.57	7.43	10.22	11.14	13.93	21.18
0.544	13.8	BT-5	...	1.36	1.80	2.04	2.44	2.48	2.79	3.01	3.72	3.90	4.12	4.64	4.76	5.57	7.43	10.22	11.14	13.93	21.18
0.544	13.8	BT-5	...	1.36	1.80	2.04	2.44	2.48	2.79	3.01	3.72	3.90	4.12	4.64	4.76	5.57	7.43	10.22	11.14	13.93	21.18
0.544	13.8	BT-5	...	1.36	1.80	2.04	2.44	2.48	2.79	3.01	3.72	3.90	4.12	4.64	4.76	5.57	7.43	10.22	11.14	13.93	21.18
0.544	13.8	BT-5	...	1.36	1.80	2.04	2.44	2.48	2.79	3.01	3.72	3.90	4.12	4.64	4.76	5.57	7.43	10.22	11.14	13.93	21.18

Posted by Ted at October 26, 2002 01:32 PM | TrackBack