# Working out scale

#### Karl

##### Well-Known Member
TRF Supporter
I would like to build a scale AMRAAM. (Im so addicted to building AMRAAM's!)

My bodytube dia is 70.9mm and the full scale AMRAAM dia is 177.8mm. Could you please show the math aswell so I can see what's going on.
Thanks
Karl

#### cls

##### Well-Known Member
hey Karl,

71mm divided by 178mm gives a about 40% scale, or 2.5:1 scale.

so if the real AMRAAM is say 5 meters long & 178mm diameter, then your 2.5:1 scale model will be (5 / 2.5 == 2) 2 meters long and 71mm diameter.

cut the fins' dimensions by 2.5 as well and they will be in "scale".

there is an issue with scaling though: the ratio of areas changes. For example, at full scale the fins are a certain size, which for stability is the "right size" for the airframe tube size. at an up or down scale, though, the fin area may be too little or too much for the airframe tube.

short answer: simulate it! or post something on TRF and maybe someone will help sim.

#### Karl

##### Well-Known Member
TRF Supporter
Thanks ! Ill Rocksim it now .

Erm , I wanted this to be my Level 2 project , so thats a 'J' , 'K' or 'L' impulse motor , say for instance , is a J impulse motor available in a Pro38 form?
-Karl

#### vjp

##### Well-Known Member
Originally posted by Karl
I would like to build a scale AMRAAM. (Im so addicted to building AMRAAM's!)

My bodytube dia is 70.9mm and the full scale AMRAAM dia is 177.8mm. Could you please show the math aswell so I can see what's going on.
Thanks
Karl

Hi Karl.

Since your BT is 70.9mm, and the original is 177.8mm, the scale is 177.8 / 70.9, or 1/2.5.

So, all other measurements on the original should be divided by 2.5 to obtain the scale equivalent for your project. i.e., if the subject's nose cone was 1200mm long, divide that by 2.5 giving a scale nose cone length of 480mm, and so on.

Angles do NOT get divided - angles always stay constant with scale. Probably obvious, but I have seen the question asked - so it's best to state that explicitly.

(Note - conversely, sometime people give scale as a "percent" of the original - in your case, you are dealing with a 40% scale model, so all original measurements are multiplied by 40% or 0.40, which is the same as dividing by 2.5).

#### cls

##### Well-Known Member
Karl - Cesaroni makes an awesome 38mm 6-grain J400. my son's Skunkworks Skeeter did "just fine" with one of those on Sunday

if you really want to move up to K & L then put a 54mm mount in your rocket. and be prepared to glass it.

do you need the ENG files for Cesaroni motors? I think I found them on the Tripoli web site ...

EDIT: duh, never mind that, just go to EMRR and look under "Rocksim Library", the Ricearoni motor files are here

#### Karl

##### Well-Known Member
TRF Supporter
Originally posted by cls
Karl - Cesaroni makes an awesome 38mm 6-grain J400. my son's Skunkworks Skeeter did "just fine" with one of those on Sunday

if you really want to move up to K & L then put a 54mm mount in your rocket. and be prepared to glass it.

do you need the ENG files for Cesaroni motors? I think I found them on the Tripoli web site ...

EDIT: duh, never mind that, just go to EMRR and look under "Rocksim Library", the Ricearoni motor files are here

Im not sure if we have a supplyer over here in the UK , thanks for the replys , I think i've finaly got my head round the 'scaling' part of a rocket! I'll draw the rocket out by hand , put in all the dimensions , scan it , and put it on here so you can check if i've got it right .
Thanks once again
-Karl

#### Micromeister

##### Micro Craftman/ClusterNut
TRF Supporter
Karl:
Hope this doesn't confuse the issue, I've alway found it easier to work with a mulitplier instead of dividing by a scale factor.

to find the Scale do what everyone has suggested divide the prototype dimension by your model dimension in this case 177.8/70.9 = 2.5077 or 1 : 2.5077 scale

to find the multiplier simply reverse the process divide 70.9/177.8 = .3987626 you can now multiply all the prototype dimensions by this number to find all your model dimensions. If you use one of the scale work sheets listing all the prototype dimensions first, it's possible to enter the multiplier in the calculator then run all the numbers. sure makes it quicker for me.

Hope this helps

#### Fore Check

##### Well-Known Member
I'm with you, John.

When I do an Upscale from plans, that's how I do it.

For instance:

If the plan rocket is BT50 based, it's diameter is .976 inches.

If I want to build it BT70 based, my rocket will be 2.217" diameter.

My rocket will be 2.217/0.976 = 2.271 upscale factor.

Multiply all the dimensions by 2.271, you've got it.

The math is the same no matter if your upscaling (in my example) or downscaling (in your example, Karl.)

Karl, your downscale factore is exactly as Micromister said above: multiply all the scale dimensions for the actual AMRAAM by .3987626 and you've got it for what you're building.

Hope to see pics soon!

#### sandman

##### Well-Known Member
Yep, the "multiplier" is the easiest way to do it.

Like My Little Joe II kit. just multiply all the real world dimensions by .0256

Easy!

sandman

##### Well-Known Member
It's worth noting that 1 inch = 2.54 centimetres. So try to get plans for the AMRAAM in inches. Then, where the plans say inches, you read centimetres. (I'm guessing that the original plans were in inches because 177.8mm, the full size diameter that you quote, is 7 inches. )

I found a similar coincidence when building a derivative of the V-2. The real V-2's diameter was about 1.6 metres, an Estes BT-60 tube is about 1.6 inches, so get plans measured in metres and measure your model in inches.

#### Micromeister

##### Micro Craftman/ClusterNut
TRF Supporter
I Still think it's unfortunate we are the only nation in the workd still using the english measuring system, even the English don't use the english system.
I kinda like being only 1.876m tall and 142.8 kilos... doesn't make me any smaller but well it's the perception thing AhHaha

#### Karl

##### Well-Known Member
TRF Supporter
Well heres the picture I promised.
-Karl

#### Peter Alway

##### Well-Known Member
Just a note about converting units and scaling at the same time. You can just use your model dimensions in the system you use to build and the prototype dimension in the units your source uses. So you can buid to a scale of 70.9 mm:7.0 in. Just multiply each prototype dimension (given in inches) by 10.13 to get a model dimension in mm.

IT's good to see someone building an AMRAAM that is actually scaled down from the real thing, and not scaled up from an inaccurate kit (there seems to be a tradition of selling AMRAAM kits with nose cones that are twice as long as they should be).

At the risk of being a jerk--Hey, that's my drawing! I was going to complain about my name being cut off until I noticied it was cut off where I originally uploaded it. D'oh! I did upload it specifically so it could be freely used for just this purpose, though. It's good to see it put to use.

#### fehskens

##### Well-Known Member
I'm surprised no one mentioned this already, so I want to clear up this common misconception. Yes, it's true that areas scale as the square of the scale factor, but the relationships between the ares remain unchanged. Hence, the CP does not move due to scale changes. It may move a small amount (or more likely, the CP location as a function of angle of attack may change) due to the change in the Reynolds number (air seems "stickier" for smaller objects), but this effect is small enough to ignore. So scaling does not affect stability (discounting of course, active stabilization in the prototype vs. passive or aerodynamic stabilization in the model).

#### Micromeister

##### Micro Craftman/ClusterNut
TRF Supporter
Originally posted by Peter Alway
IT's good to see someone building an AMRAAM that is actually scaled down from the real thing, and not scaled up from an inaccurate kit (there seems to be a tradition of selling AMRAAM kits with nose cones that are twice as long as they should be).

At the risk of being a jerk--Hey, that's my drawing! I was going to complain about my name being cut off until I noticied it was cut off where I originally uploaded it. D'oh! I did upload it specifically so it could be freely used for just this purpose, though. It's good to see it put to use. [/B]

HEhe: I was just about to compliment Karl and the excellent drawing, and ask if he got the info from you.

I built mine for the actual dimesions including the boattail.. couse it's a Micro-Maxx powered model

I have to take exception to your stability post fehskens; the CP may stay nearly the same but differing construction material, solid or hollow nose cones, transitions, etc can and does alter the CG greatly. Just because the real vehicle flys, does not by any means mean an exact up or downscale model will be stable. AMRAAM is no exception.

#### Karl

##### Well-Known Member
TRF Supporter
Originally posted by Micromister
HEhe: I was just about to compliment Karl and the excellent drawing, and ask if he got the info from you.

I built mine for the actual dimesions including the boattail.. couse it's a Micro-Maxx powered model

I have to take exception to your stability post fehskens; the CP may stay nearly the same but differing construction material, solid or hollow nose cones, transitions, etc can and does alter the CG greatly. Just because the real vehicle flys, does not by any means mean an exact up or downscale model will be stable. AMRAAM is no exception.

I'll SpaceCAD it now to see what it says LOL A micromaxx version , wow! How does it fly?

Originally posted by Peter Alway
At the risk of being a jerk--Hey, that's my drawing! I was going to complain about my name being cut off until I noticied it was cut off where I originally uploaded it. D'oh! I did upload it specifically so it could be freely used for just this purpose, though. It's good to see it put to use.

Yeah , I've just re-visited your website and only 1/2 of the bottom righting to be seen!

-Karl

#### hokkyokusei

##### Well-Known Member
there is an issue with scaling though: the ratio of areas changes. For example, at full scale the fins are a certain size, which for stability is the "right size" for the airframe tube size. at an up or down scale, though, the fin area may be too little or too much for the airframe tube.

Are you sure? CP is not effected by scale, so I don't see how your statement can be true?

#### CTimm

##### Well-Known Member
Originally posted by Peter Alway
I was going to complain about my name being cut off until I noticied it was cut off where I originally uploaded it.

At least you were kind enough to leave the top half of my name showing.

Chris Timm

#### Elapid

##### Well-Known Member
if RockSim had an Upscale and a Downscale button?
automatic scaling to the next body tube size or custom sizing
automatic redrawing of the plans, selecting the next size up on all the parts, i.e. centering rings, finstock, motor mounts...

that would be cool!

#### cls

##### Well-Known Member
CP is not effected by scale, so I don't see how your statement can be true?

CP is not affected by scale, but the ratio of the areas is. roughly, Borrowman stability equations work by surface area. for example, let's compare Apogee's Blue Streak with my daughter's 3x upscale. according to rocksim,

Blue Streak 1x with an A6-4 has Borrowman stability of 1.85 (cutout stability of -1.8!);

Blue Streak 3x with an E9-6 has Borrowman stability of 5.7 (cutout stability of -0.07).

so, by Borrowman equations, Blue Streak 3x is clearly overstable. in flight it shows that by weathercocking somewhat more than 1x does in the same wind.

that's the reason you always want to run the numbers for the scale rocket - it could save a marginally stable design (V2, AMRAAM, BullPup, etc.) from becoming unstable. anyways it doesn't hurt to run the numbers and some of us even think it is fun!

(above I quoted the cutout stability numbers to show that the ratio of areas changes with scale.)

#### powderburner

##### Well-Known Member
I think the comments made by fehskens were basically correct. It would seem that he was assuming that the overall c.g. would also scale to the same relative postion when he made his comment about stability not changing.

Karl, if you are building a large-scale model of the AIM-120, did you know that the body diameter is not a constant seven inches?
Early AMRAAMS were experiencing high failure rates in the radar system in the nose of the missile because of excessive vibrations. (The missiles are carried on the F-15 Eagle with the tip of the missiles nose even with the lip of the aircrafts air intake duct---in supersonic flight the missile was being pummeled by shock waves and spilled airflow from the inlet.) The fix was to beef up the structural body of the missile by making it thicker over the main electronics section (about half-way between the nose and forward fins). Somewhere in a file cabinet I still have the Aviation Week & Space Technology article that talks about this problem.

Anyway, if you look closely at photos of the missile (they are often in AW&ST) you can see the thickness difference. By incorporating this little detail in your scale notes, you could out-score your competitors?

BTW, does anyone have any scale details of the fin contours? I am tired of seeing flat slab-fins. I have an official Raytheon drawing with all the data, but I am not authorized to release the information (&^[email protected]**^!) so does anyone else have it?

#### fehskens

##### Well-Known Member
Powderburner's right; I did (incorrectly) assume the CG would not be affected by scaling, and it clearly is (because masses change as the cube of the scale factor). So the first part of my posting is correct, the CP location will not be affected by scaling, but the last sentence is incorrect; stability may be affectd by scaling, not because of the areas, but because the CG may move relative to the unaffected CP. In the A vs. E example, the difference in stability margin is almost certainly due to the large difference in relative masses of the engines; if you look at the CP location for two versions, they should be nearly identical, but the CGs will differ.

len.

#### cls

##### Well-Known Member
I simmed with an A instead of a C because it's more comparable, relative weights of rocket vs. motor. change in CG of Blue Streak 1x with a C6-7 is even larger.

comparing stability without motors is silly, but that way it is easy see how the CP moves a bit because of scaling.

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