apparent size at a given distance

[av8boy]

The “distance to the horizon” discussion on another thread put me in mind of something that’s been (quietly and somewhat infrequently) bothering me for years now:

In my air force days I recall seeing posters which illustrated how large an aircraft appeared at a particular distance. Something like “this dot represents the apparent size of a T38 at three miles.” Various ranges were shown and the idea was to illustrate just how quickly that dot can close on your aircraft and why it’s best to pay attention while it’s still a dot and scan in the manner taught.

For the life of me I can’t find examples of this graphic anywhere. Nor can I determine how to calculate such a thing. I’ve considered things like inverse square, working out degrees of arc, etc., however, I can’t seem to manage it. I’m pretty certain I could work it out empirically, but I’d like to be able to do it in a predictable manner without things like a full-sized replica of a A380 set up on a hillside three miles distant, and me holding a ruler at arm’s length…


Thoughts?

[Capt Pit Bull]

Well, for a poster of a dot to equal a certain sized object at a certain range, you first have to fix the distance of the viewer to the poster.

e.g. you have to say something like "stand 3 feet in front of this picture, and then this dot = the apparent size of a t-38 at 3 miles"

Once you've done this, its just an inverse law. (not an inverse square.)

As our imagined image is 3 miles away instead of 3 feet, we just need a 1 / 6,080 th sized T-38 picture, and jobs a good 'un.

(1 mile = 6080 feet , so if you moved a full sized t-38 from 3 feet away to 3 miles away, it would shrink by a factor of 6,080.)

That any use?


CPB

[Moe Syzlak]

A milliradian (mil) subtends 6 feet at one mile, so if the T-38 wingspan was 24 feet then it would be 4 mils at a mile, 8 at half a mile (1000yds) and 16 at 500 yds 32 at 250 Yds etc. 1000 mil = 1 radian ~= 58 degrees.

[av8boy]

Yes! Thanks to both of you!

Yeah, as I recall, the posters always indicated some sort of particular viewing distance.

I'm off to pull my T38 three miles for a look. Thanks again.

[Yellow Sun]

Or to put it another way:

1 Minute of Angle (MoA) subtends approx. 1" at 100 yds

60 MoA = 1 degree

YS

[av8boy]

Again, thank you. And I get to use the term, "subtend" as well!

As an aside, didn't Mr. Draper serve aboard a sub-tender?

:confused:

[-IBLB-]

@ av8boy

look at the last page of this AC 90-48C (http://www.airweb.faa.gov/Regulatory_and_Guidance_Library/rgAdvisoryCircular.nsf/0/7373cdbc7158f4c286256a03006e1551/$FILE/AC90-48c.pdf)


I'm pretty sure either ASF, or AOPA had a newer version of it, but i can't seem to find it.


-IBLB-

[Fg Off Max Stout]

OK av8boy, the other guys are pretty damn close with the inverse law but to be exact, well here goes:

The apparent size of an object depends on the angle it subtends at your eye. Draw a right angled triangle and do a bit of trig. Let theta be the angle, s be the size of the object eg wingspan and therefore a constant, and d, the distance.

Tan(theta)=(s/d)

where theta is in radians, s and d in the same units of linear measurement.

Rearrange this you get

Theta=Arctan(s/d)

Theta and d being your variables.

You can therefore see that the apparent size is based on an Arctangent curve. I used excel to knock up the illustration below based on a 50ft wingspan. That's how sad and bored I am right now.

http://i6.photobucket.com/albums/y224/bofns/Size2.gif

The RAF have a poster similar to the one you describe and as the graph shows, the gist of it is that you may see a spec in the distance with no discernable growth rate,and be unconcerned by it. The trouble is that as it gets closer it suddenly 'blooms' and its size goes through the roof. By this time you really notice it, it's filling your canopy and your about 3 seconds from hitting it.

There is an amazing video of a near miss like this. You can see the dot for ages and then whoomph, you can't see anything else. It must be out there somewhere on the net. The moral of the story is react early and don't ignore the little dots.

[747FOCAL]

Misleading title, Jerricho will think this should be in Jet blast......

:E

sorry to divert, but could not resist.....:)

[aerolearner]

Similar diagram from a different source (Air Force Pamphlet 127-1, Vol II):

http://www.geocities.com/aircraftfire/temp/midair1.jpg

http://www.geocities.com/aircraftfire/temp/midair2.jpg


Excel (English edition) file to draw the diagram with different wingspans and closure rates:

http://www.geocities.com/aircraftfire/temp/midair.xls

[av8boy]

Wow! You guys are good. Thanks!