Aeronautics 1110x 2d-slides

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Prof. dr. ir. Jacco Hoekstra Geopoten’al & geometric al’tude Introduc)on to Aeronau)cal Engineering

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Aeronautics 1110x 2d-slides

Transcript of Aeronautics 1110x 2d-slides

Page 1: Aeronautics 1110x 2d-slides

Prof.  dr.  ir.  Jacco  Hoekstra  

Geopoten'al  &  geometric  al'tude  

Introduc)on  to  Aeronau)cal  Engineering  

Page 2: Aeronautics 1110x 2d-slides

The  hydrosta'c  equa'on  Geopoten'al  al'tude  Assump5on:  g0  =  constant  

p + Δp

m· g0

p

Δh

Area A

dp  =  -­‐ρg0dh  

p + Δp

m· g

p

Δhg

Area A

dp  =  -­‐ρgdhg  

Geometric  al'tude  g  varies  

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Geopoten'al  &  geometric  al'tude  

-­‐  We  use  geopoten5al  al5tude  as  default(easier)  

-­‐  Nota5on:      h  =  geopoten'al  al'tude  (default  but  wrong)          hg    =  geometric  al5tude  (real  al5tude)  

-­‐  What  is  the  difference?  How  to  convert?  -­‐  Let’s  derive  the  rela5on….  

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So  what  is  the  effect  of  our  approxima'on?  

eG

e G

Rh hR h

=+

6378 20

e

G

R kmh km=

=Let’s  try  with:  

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So  what  is  the  effect  of  our  approxima'on?  

eG

e G

Rh hR h

=+

6378 20

e

G

R kmh km=

=Let’s  try  with:  

6378000 20000 19 937.56378000 20000

0.3%

h m

Error

= ⋅ =+

=

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Geopoten'al  &  geometric  al'tude