Form for Sight Reduction

Date: GMT watch: Body: WE: (f/s)

GMT (-f/+s):

DR lat (L): DR long (l):

GHA at  hrs  ^{∘}  ′
Incr for  ^{∘}  ′
Corr’n for v =  0^{∘}  ′

GHA

Dec’n at  hrs  ^{∘}  ′ N or S
Corr’n for d =  0^{∘}  ′

Dec’n N or S

H_{s}  ^{∘}  ′
I_{c}  ^{∘}  ′
Dip corr’n  ^{∘}  ′
HP  ^{∘}  ′
Refrac’n  ^{∘}  ′
H_{o}

GHA  ^{∘}  ′
l (+W/-E)  ^{∘}  ′

LHA d (+/-)

H_{c} = sin^{−1} (sin L sin d + cos L cos d cos LHA) =  ^{\overline{∘}}
Z = cos^{−1} (\frac{sin d − sin L sin H_{c}}{cos L cos H_{c}} ) =  ^{\overline{∘}}
Body to west  Body to east
North latitude Z_{n} = 360 − Z =  Z_{n} = Z =
South latitude Z_{n} = 180 + Z =  Z_{n} = 180 − Z =

\begin{matrix}H_{o}  ^{∘} & ′ \\ H_{c}  ^{∘} & ′ \\ H_{o} − H_{c}  ^{∘} & ′ \\ a (+t/-a) \end{matrix}  \begin{matrix}Z = \\ Z_{n} = \end{matrix}

Form for Great Circle Sailing

Date:

Dest (L_{1}): ± (l_{1}): POD (L_{0}): (l_{0}):

t = l_{1} − l_{0}:
D(^{∘}) = cos^{−1} (sin L_{0} sin L_{1} + cos L_{0} cos L_{1} cos t) =
D(nm) = 60D(^{∘})  =

Take L_{0} to be positive. If L_{0} and L_{1} have the same name, then take L_{1} as positive also. Otherwise, take L_{1} to be negative.

θ_{0} = cos^{−1} (\frac{sin L_{1} − sin L_{0} cos D(^{∘})}{cos L_{0} sin D(^{∘})}) =

Take L_{1} to be positive. If L_{0} and L_{1} have the same name, then take L_{0} as positive also. Otherwise, take L_{0} to be negative.

θ_{1} = cos^{−1} (\frac{sin L_{0} − sin L_{1} cos D(^{∘})}{cos L_{1} sin D(^{∘})}) =

Dest west of POD Dest east of POD

L_{0} north C_{0} = 360 − θ_{0} =  C_{0} = θ_{0} =
L_{0} south C_{0} = 180 + θ_{0} =  C_{0} = 180 − θ_{0} =

Dest west of POD Dest east of POD

L_{1} north C_{1} = 180 − θ_{1} =  C_{1} = θ_{1} =
L_{1} south C_{1} = 180 + θ_{1} =  C_{1} = 360 − θ_{1} =

Form for Mid-Latitude Sailing

Date: Dest (L_{1}): (l_{1}): POD (L_{0}): (l_{0}): ΔL(′): Δl(′):

L_{m} = \frac{1}{2} (L_{1} + L_{0}) =

θ = tan^{−1} (\frac{|ΔL|}{cos(L_{m})|Δl|}) =

D = \sqrt{(ΔL)^{2} + (cos(L_{m})Δl)^{2}} =

Dest west of POD Dest east of POD

Dest north of POD C = 360 − θ =  C = θ =
Dest south of POD C = 180 + θ =  C = 180 − θ =

Form for Noon Sight

Date: GMT watch:

WE: (f/s) GMT (-f/+s):

GHA at  hrs  ^{∘}  ′
Incr for  ^{∘}  ′
Corr’n for v =  0^{∘}  ′

GHA

Dec’n at  hrs  ^{∘}  ′ N or S
Corr’n for d =  0^{∘}  ′

Dec’n N or S

H_{s}  ^{∘}  ′
I_{c}  ^{∘}  ′
Dip corr’n  ^{∘}  ′
HP  ^{∘}  ′
Refrac’n  ^{∘}  ′

H_{o}

North Dec’n  South Dec’n
Sun to north L = H_{o} − 90 − |d| =  L = H_{o} − 90 + |d| =
Sun to south L = 90 − H_{o} + |d| =  L = 90 − H_{o} − |d| =

GHA < 180  GHA ≥ 180
l = GHA = (W)  l = 360 − GHA = (E)