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I am trying to understand this technical note, specifically problem 1 on page 4.

I am quite happy with everything up to equation 2 on page 5. I don't understand where the figure .39D 2/3 has come from nor 48D 2/3 in equation 3.

Can anybody else see where these figures have come from? I've been looking at this for sometime. I realise it is quite a long question but I would be grateful for any help.

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It would probably help getting people interested in answering if you wrote something about what the hell this is about instead of just expecting people to click through to a PDF download just to find out whether it is something they know anything about. – Henning Makholm Feb 5 '12 at 22:54
up vote 1 down vote accepted

The complicated expression for $HP$ comes from page 3.

$HP = .39 \; D^{2/3} \quad (2)$ is just the multiplication and division of the numbers in the complicated expression

$D - 48\; D^{2/3} = 42000 \quad (3)$ comes from substituting the result of $(2)$ into $(1)$ which was $15000 +44 \; HP = .357 \; D$ and multiplying through by $1/0.357$ , with some slight rounding.

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Thanks for your reply. I'm happy with equation 2 now, I think I was just having some sort of mental block. But I am still struggling with part 3. Where does 48 come from? – DNN Feb 6 '12 at 21:28
I realise that 15000 * 1/0.357 = 42000 – DNN Feb 6 '12 at 22:14
$44 \times 0.39/0.357 = 48.067\ldots \approx 48$ – Henry Feb 7 '12 at 1:40
Thanks, got it. – DNN Feb 7 '12 at 8:25

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