my maths has gone wrong

[head_girl]

Help!

I got into a discussion about geometry over too many glasses of Hunter Valley red. My head hurts.

Length of an arc = radius x angle in radians, correct?

Well if I’m flying at constant height at 405ft/sec TAS in one minute I’ll have flown 24300ft in distance. [Based on 240 kts by the way].

The distance is speed in knots / 60 = 240/60 = 4nm, correct?

So if I have turned around 180 degrees in direction in that time that is pi radians, correct?

Therefore my radius of turn must be 7735ft, correct?

Going on from this (V^2)/Rg = tan bank angle, so my bank is 0.66 radians. Suppose g is 32 ft/sec/sec and there are say 57.3 degrees in a radian the bank angle is 38 degrees.

So a rate one turn at 240 knots is 38 degrees of bank?

Where have I gone wrong in my maths which I thought I was so good at?

Suffering from the wrath of grapes


h_g

[enicalyth]

h_g

Tan bank angle may be 0.66 but sin angle and tan angle only approximate to angle in radians when the angle is small. So if tan bank = 0.66 then bank = .58 radians or about 33 degrees.

Is this where you have gone wrong? Too much wine, you make mistakes and then you can look at the answer for ever and a day and gloss over the same mistake without seeing it.

Are you in today, then? Give us a call!

Best rgds

E

[head_girl]

What a twonk! it's only with small angles like angle of attack that you can apply the approximation. I should be able to do things from first principles but like you say, spotting a mistake can be hard if your sure your right. Go on, say it "the young generation are dumbed down!" [V nice wine though.]

Yup. In. Probably same building.

[john_tullamarine]

Given a choice between percolating the brain in a fine Hunter drop, or straining it with maths, that choice, surely, is a programmed decision .. but, then again, I'm a Cessnock lad, well-steeped in the local vineyards around the aerodrome and coal mining ...... in fact, had my very first fixed wing flight from there .. and finished my PPL over the way at West Maitland .. a long time ago, now. Memories of Stan, Jack the Black, Bernie, et al.

[head_girl]

Omigod John, this is spooky. I'm having drinks with a friend [guess] even now and of course we talk. The friend who helped me fly? So when I tell you that you went to school where he lives you know who I am on about who is pouring the Hunter Valley drinks? You know Moonan Flat just up the road from Cessnock? Well the Victoria is a fave watering hole of his and now you say you're from Cessnock too. This is too scary by half.

Apart from the nice wine [sip] did nobody else spot how I slipped glibly from tan angle to radians? I can't believe I did that.

But Omigod again!