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A 1:48 scale model -- what is the distance you are looking at it?


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Hello forum,

If you were looking at a 1:48 scale model of an F-4 Phantom II, what would be the distance of the F-4 if the fighter was real and not a model?


An F-4 has a length of 63 feet. Using this calculator, 63 feet in 1:48 scale is 1.3125 feet:


https://www.inchcalculator.com/scale-calculator/


So the length of the Phantom is 1.3125 feet in 1:48 scale. But in real life, at what distance would the Phantom have to be to have a length of 1.3125 feet?


Thanks for the help,


Chris
 

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It depends. 

 

🙂

 

Obviously, the length of a real Phantom will always be 63 ft, no matter what distance it is viewed from. 

 

I think the criteria you need to consider is one of the subtended angle. In other words, if a model is viewed at a specific distance and subtends a specific angle, what distance would the real aircraft have to be viewed from to subtent the same angle?

 

Fortunately the geometry scales linearly so, if you view a 1:48 scale model from 1 foot away, the real thing will appear to be the same size when viewed from 48 feet.  

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7 hours ago, habu2 said:

It depends. 

 

🙂

 

Obviously, the length of a real Phantom will always be 63 ft, no matter what distance it is viewed from. 

 

I think the criteria you need to consider is one of the subtended angle. In other words, if a model is viewed at a specific distance and subtends a specific angle, what distance would the real aircraft have to be viewed from to subtent the same angle?

 

Fortunately the geometry scales linearly so, if you view a 1:48 scale model from 1 foot away, the real thing will appear to be the same size when viewed from 48 feet.  

 

I learned a new word today. Subtend, had to look that one up. Thanks habu2!

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7 hours ago, chris2019 said:

Habu2,

 

And for a 1:72 scale model, it would be like looking at a Phantom at 72 feet away from you?

 

 

 

To answer your question, looking at a 1/72 model 1 ft away is roughly* the same as looking at the real thing from 72 ft away. 

 

*Habu's way of thinking is the right way to go. At the risk of being overly pedantic, see the pic below. It is a top view. Basically, when you are going up and down the scales, you want to keep theta unchanged. Say the length of the airplane is 60ft (length) and you are sitting 100 ft away from it (dist). If the length was made 6 ft (imagine a 1/10 model), distance would need to be 10 ft to preserve the same angle. 

 

This is a simplification though, and does not take into account things like camera field of view etc. if all this is about photography. Also, if it is about the level of detail you would see on the scale model (e.g., to make an argument for or against rivets), this type of simplification is not going to capture everything at play here (especially if theta is wide, i.e., distance is short relative to length, as then you would need to think about the huge difference between the closest point on the airplane to your eye vs the farthest point, the amount of detail will be very different). For the most part, it is a good approximation though. 

 

 

a.jpg

Edited by Janissary
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  • 2 years later...

I know this is an extinct conversation now but I had to mention that the points being made are incorrect.  1:48 is NOT the same as looking at something from 48 feet away.

 

Imagine a Spitfire parked in an end zone and you're standing on the 16 yard line (48 feet).  Is the Spitfire going to appear to be the size of a model airplane?  No.  

 

1:48 (or whatever scale) simply refers to the fraction - in this case 1/48.  Everything in that scale is 48 times smaller than it's real life counterpart. (A piece measuring 48 inches in real life would be 1 inch on the model.)

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I think you’re confused.
 

1: Scale is not a fraction, it’s a ratio. Semantics? Maybe…

 

2: it was explicitly stated that a 1:48 model viewed at 1 ft distance would appear the same “size” (subtending the same viewing angles) as a 1:1 jet at a distance of 48 feet. 

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I understand what you're saying and it's very well described, I just don't agree.  That would mean that if you were standing next to your car and took two steps away it would appear to be 1:2 scale.  Looking at a car from 10 yards away doesn't make it appear the size of a 1:32 model.  (As an additional aside, that's presupposing that feet would be the unit of measurement whereas it would seem more likely be the metric system.)

 

People standing 48 feet away don't appear to be one inch tall.  

 

I drove to an air force museum the other day and from about 100 yards away there was an F-15 on display outside.  It did not appear the size of a 1:300 scale model.

 

Regardless, very educated argument on your behalf and, who knows, I could well be wrong.

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Just to belabor the point: Imagine you were at one end of a football field and at the other end was a B-17 (300 feet away).  By your calculation the B-17 would be 1:300 scale, or about the size of a half-dollar and that obviously wouldn't be the case.

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11 hours ago, otterblue32 said:

<...> People standing 48 feet away don't appear to be one inch tall.  <...>

 

You're right. They don't appear to be one inch tall. But that isn't really the question. The question is: are people standing 48 feet away perceived to be as tall as a 1/48 figure held one feet away from your eye?

One feet to 48 feet. Actually one "unit of measurement" to 48 "units of measurement". Imperial/metric doesn't matter here. As long as you're keeping the units in your experiment constant, it doesn't matter which one you use.

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FWIW, here's the result of a quick experiment:

 

https://www.facebook.com/photo?fbid=10208455286176377&set=a.1559955255486

 

The pic is of a 1/32 and a 1/48 Hellcat.  For the sake of argument, consider the 1/32 to be full size, and the 1/48 to be a 2/3 scale model.  The full size one is approximately 3 feet from the camera lens, and the 2/3 scale model is approximately 2 feet away. (that's all the room I had on the table, so it'll have to suffice).  Setting aside the fact that I didn't raise the closer model so that the vertical angles were the same, and the imprecision of my model placement and the fact that I probably should have used the camera's focal plane as a reference rather than the lens face, the 1/48 is approximately the same visual size as the slightly farther away 1/32 model.  So yes, a full size object viewed at 48 feet away should appear to be the same size as a 1/48 scale model of that object viewed at 1 foot away.

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My point is the model scale IS a fraction.  A 1/72 scale Spitfire's wingspan is (a little over) 6 inches.  6 X 72= 432.  432 inches is 36 feet, which is the wingspan of a real Spitfire (37 feet).

 

I contend that the scale doesn't relate to the visual size of viewing from a distance.  

 

Something that is in 1/2 scale would be half the original size but it wouldn't be comparable to looking at that object from 2 feet, or 2 meters, away.

 

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8 minutes ago, otterblue32 said:

My point is the model scale IS a fraction.  A 1/72 scale Spitfire's wingspan is (a little over) 6 inches.  6 X 72= 432.  432 inches is 36 feet, which is the wingspan of a real Spitfire (37 feet).

 

I contend that the scale doesn't relate to the visual size of viewing from a distance.  

 

Something that is in 1/2 scale would be half the original size but it wouldn't be comparable to looking at that object from 2 feet, or 2 meters, away.

 

But, the idea isn't that you're viewing at 2 feet or 2 meters away, for a 1/2 scale model to APPEAR to be the same size as the full-scale one, you would be viewing it at 1/2 the distance you're looking at the full-size one.  If you have a 3/5 scale model, and a viewing distance of X feet to the real thing, viewing the model at 3/5 X will make the model APPEAR to be the same size as the real one.  A 1/72 scale model at 1 foot viewing distance appears to be the same size as a full-scale version of that model at 72 feet. If you look at the same 1/72 model at 2 feet, then it would have the same apparent size as the real thing 144 feet away.  

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Yes, I know.  That's the point I'm contending: that 1/72 isn't the same as viewing the same object from 72 feet away.  My example would be that a B-17 a football field away (100 yards away) would not appear to be 1/300 scale (or the size of a fifty-cent piece).  For example, viewing something from twice the distance does not decrease it's appearance by 50%.

 

Whereas, the fraction is proven to relate to the actual size of the model: an airplane model at 1/72 scale is 72 times smaller than it's real life counterpart.

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If you were on one end of a football field, you could still see the people at the other end (though obviously much smaller) - but how would a B-17 then appear to be 1/300 scale -  the size of a coin?

 

Model scales directly relate to size (which is easily proven by measuring a model and then doing the math) - not appearance at a distance.  The erroneous point is something viewed from twice the distance would be considered 1/2 scale - which is half it's original size.  If you were talking to a friend from 1 foot away and he backed up to 2 feet away, he would not appear to be 50% smaller.

Edited by otterblue32
further explanantion
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No one is saying that a B-17 300 feet away looks 1/300 scale, and no one is claiming that something at twice the distance is 1/2 scale.  I think you’re missing the entire concept; a 1/300 scale B-17 viewed from one foot away will look the same size as a full scale one 300 feet away.  It’s all based on the geometric concept of similar triangles.   

 

It’s about relating the viewing distance to a model to a distance that the real article would appear to be the same size, which is based on what scale the model is.  To take your B-17 example; if the real thing is 300 feet away, then a 1/48 scale model placed 300/48 feet away will appear to be the same size, or a 1/72 model placed 300/72 feet away will look the same size.   The RELATIVE viewing distances are what matters, not the absolute, and the relative distances are based on the scales.

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Think of it this way. If you go to an airshow and take a picture of a parked aircraft, and then make a 1/72 diorama of the aircraft and a model you taking a picture of that aircraft 1/72 the distance away, then the hypothetical photos taken by you and the model you will look the same.

 

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59 minutes ago, Joe Hegedus said:

a 1/300 scale B-17 viewed from one foot away will look the same size as a full scale one 300 feet away

 

 

That's what I'm arguing is incorrect: that a 1/300 B-17 (from a foot away) will NOT appear the same size as a real B-17 300 feet away.  Again, imagine a real B-17 at one end of a football field and you at the other - would it appear to be the same size as the 1:300 model in front of you?  The actual B-17 would appear much larger.

1 hour ago, Joe Hegedus said:
1 hour ago, Joe Hegedus said:

To take your B-17 example; if the real thing is 300 feet away, then a 1/48 scale model placed 300/48 feet away will appear to be the same size, or a 1/72 model placed 300/72 feet away will look the same size.

 

By 300/48 you mean 6 feet I guess (as in 300 divided by 48)?  So a 1/48 scale B-17 placed six feet away will look the same as a real one 300 feet away?  I don't think that makes sense.

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1 hour ago, spejic said:

Think of it this way. If you go to an airshow and take a picture of a parked aircraft, and then make a 1/72 diorama of the aircraft and a model you taking a picture of that aircraft 1/72 the distance away, then the hypothetical photos taken by you and the model you will look the same.

 

 

That's a great way of explaining it but I'm not sure I fully grasp it or that it negates my original point (although maybe it does and I'm missing the point altogether - it's happened before).

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1 hour ago, otterblue32 said:

 

That's what I'm arguing is incorrect: that a 1/300 B-17 (from a foot away) will NOT appear the same size as a real B-17 300 feet away.  Again, imagine a real B-17 at one end of a football field and you at the other - would it appear to be the same size as the 1:300 model in front of you?  The actual B-17 would appear much larger.

By 300/48 you mean 6 feet I guess (as in 300 divided by 48)?  So a 1/48 scale B-17 placed six feet away will look the same as a real one 300 feet away?  I don't think that makes sense.

It makes perfect sense.  Do you understand the concept of similar triangles?  It's all about proportions.  The attached graphic is about as basic as I can make it to get the point across; from the viewer's location, all 3 airplanes will appear to be the same size.   

Similar triangles.jpeg

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26 minutes ago, Joe Hegedus said:

The attached graphic is about as basic as I can make it to get the point across; from the viewer's location, all 3 airplanes will appear to be the same size.   

 

Ah, yes.  Thanks for the visual.  It makes sense now.  Interesting to me, annoying to everyone else.  Case closed.

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Waaaaay back in ye olden days before CGI, filmmakers used to rely on this sort of math when constructing models for special effects shots.  (They also relied on matte painting to achieve backgrounds that couldn't be filmed on-location.)   When executed well, the "trickery" couldn't be perceived.  When executed poorly, it distracted the viewer and made the "trickery" stand out to the point that the model would be been as a "model" and ruin the intended shot.

There are other limits to "scale perception" like the fact that "water doesn't scale" and that colors become more muted the farther they are away.

My point is that since we have CGI now, we tend to forget the "visual tricks" that artists learned/relearned since the Renaissance.

 

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