How not to scale flows the cautionary tale of Howard 1|14 When - - PowerPoint PPT Presentation

How not to scale flows

∼ the cautionary tale of Howard ∼

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When was the second largest aircraft in history built? 1947

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H-4 Spruce Goose, 1947

Photo from FAA (public domain) 3|14

H-4 Spruce Goose, 1947

Photo from San Diego A&S Museum (public domain) 4|14

Figure by Clem Tillier (CC-by-sa) 5|14

Figure by Clem Tillier (CC-by-sa) 6|14

The Hughes H-4 Spruce Goose flew just once and never exceeded 20 m altitude... . . . because Hughes didn’t study this chapter.

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CC-0 Olivier Cleynen 8|14

Reference A and new machine B If CFD B = CFD A: FD B = ( 휌B 휌A SB SA V2

B

V2

A) FD A

VB VA = ( 휌A 휌B SA SB FD B FD A)

1 2

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Reference A and new machine B If CFD B = CFD A: VB VA = ( 휌A 휌B SA SB FD B FD A)

1 2

= ( 휌A 휌B L2

A

L2

B

L3

B

L3

A)

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= ( 휌A 휌B LB LA)

1 2

VB VA ∼ ( LB LA)

1 2

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CC-0 Olivier Cleynen 11|14

what about power?

Reference A and new machine B If CPB = CPA: ̇ WB = ( 휌B 휌A SB SA V3

B

V3

A)

̇ WA ̇ WB ̇ WA ∼ L2

B

L2

A

L

3 2

B

L

3 2

A

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CC-0 Olivier Cleynen 13|14

H-4 Spruce Goose, 1947

Photo from FAA (public domain) 14|14