The Angle unit - an example

Forum|Forum|15 years ago
October 4, 2010
3 replies
27132 views

Attached is a real worked example of the need for the Angle unit, extracted from todays' work.

I was computing the effect amount of extra angle of attack that will occur when an aircraft starts a "rate one turn", as this extra angle could affect where my camera is pointing. We can see the amount of banking that the plane does for a ROT, and the calculated extra angle of attack. There are references to the relevant wiki pages.

I have attached a V14 xmcdz file and the pdf of the same for all to consider.

Philip

1_Angle-of-Attack-during-Rate-One-Turns.pdf

2_Angle-of-Attack-during-Rate-One-Turns-xmcdz.zip

Other

A

AlanStevens

19-Tanzanite

Interesting! In the last line you "inadvertently" multiplied by CI instead of dividing by CI, but Mathcad didn't give any indication of this because it thought the result was dimensionless. If it had a special unit for angle the user would have been aware of the mistake immediately. As it was, "the user" inserted 'deg', thinking that the dimensionless number displayed was an angle. I now understand why you are so keen on a special unit for angle!

Alan

P

PhilipOakley

Author

1-Visitor

Alan Stevens wrote:
Interesting! In the last line you "inadvertently" multiplied by CI instead of dividing by CI, but Mathcad didn't give any indication of this because it thought the result was dimensionless. If it had a special unit for angle the user would have been aware of the mistake immediately. As it was, "the user" inserted 'deg', thinking that the dimensionless number displayed was an angle. I now understand why you are so keen on a special unit for angle!
Alan

The example is ceratinly a good one. I hadn't noticed my mistake and all afternoon I'd been saying that the bank angle and the extra angle of attack were similar, then, late in the day, I got to thinking again and felt that then AoA was a bit larger than experience showed, so I looked again and spotted the correction (as Alan correctly describes) and a far smaller 0.5 degrees comes out as the answer. It just shows what happens wihen 'believable numbers" turn up.

Doing a lot of electro optics one finds many equations that have per radian or even per steradian [with its units of Angle^2 ! ]

I have seen quite senior folk simply add in a "divide by 2pi" just to make the numbers feel right, when they had completely forgotten some part of the (angular) inputs.

The best story is of a rotary encoder with let's say 12 bit encoding. The software engineers read the number as 0 to 1 and claimed it was in radians because it was an angle (well that is what the documentation said). The system engineer then had to add a magic 2pi to the system equations to take out the conversion error. It was simpler than trying to change the documenation!

M

MJG

1-Visitor

Philip,

You present a valid (and interesting) point. One of my first reactions to this, however, was that many equations use angles as dimensionless variables. For instance, the length of a circular arc is calculated by the radius of the circle multiplied by the angle through which the arc sweeps. You would not want this equation to produce a result with units of Angle * Length, you would just want a unit of Length. Therefore, this equation would need to be written as ArcLength = Radius * (Angle / rad). I could see this as being very confusing for many users (it's certainly not how I would expect to have to set up this equation).

Not making any conclusions, just poiting out that if an Angle unit is added, it would require some good planning on PTC's part, and likely some adjustment for many users.

-Mark

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PhilipOakley

Author

1-Visitor

Mark,

If you have a look at the proposal I made in the document thread http://communities.ptc.com/message/152971 (Sep 23, 2010 1:02 PM) and its attachment, you will see that I have carefully considered the various cases where these ignored (hidden) mathematical subtleties should be covered with just 4 extra functions, such as "arc".

It is a worthwhile read. Some of the stuff about complex exponentials and branch cuts and stuff may be too much for some, but all the basics are covered.

Philip

PS I've copied the document below, just in case (I hope its the same version ;-).

1_Beyond-the-Money-Dimension---May09.doc