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10 - Second Application: a Sailing Computer
The meaning of the symbols used in these diagrams is the following:
The mathematical relationships involved in the calculation of
are given from the equations:
and
These relationships are rewritten under the following shape:
and:
Which give:
Symbol Meaning
AlphaV Visible wind angle (weather vane)
Vw Visible wind speed (anemometer)
Bs Boat speed (speedometer)
AlphaR Real wind angle
Rw Real wind speed
VMG Real boat speed against the wind, or in before the wind
MGR
VRw ,,
α
()()
[]
2/1
²sin.²cos.
VV
VwVwBsRw
αα
+−=
()
VRV
BsRw
ααα
−
=
sinsin
()
[]
2/1
cos..2.²
V
BsVwVwBsRw
α
−+=
÷
÷
÷
+=
VVR
Rw
Bs
ααα
sin.arcsin
RMG
BsV
α
cos.=
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