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

http://naca.central.cranfield.ac.uk/reports/1924/naca-tn-194.pdf

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 $p$robably hel$p$ 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.2012-02-05

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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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    $44 \times 0.39/0.357 = 48.067\ldots \approx 48$2012-02-07