Regards,

WHG

Given:

[Rt] - Radius of Driver Exit & Horn Entry ...{06}

[At] - Flare Slope Angle at Driver Exit / Horn entry

= Atan([Mt]) ... [01]

[Mt] - Flair Slope at Driver Exit

= Tan[At] ... [02]

[Ac] - Horn Coverage Angle

= Atan([Mc]) ...[03]

[Mc] - Slope of Coverage Asymptote

= Tan[Ac] ...[04]

[L] - Length of Horn Profile

Find

[Lt] - Length of Horn Profile where its Slope Angle = [At] ...{15}

[Ro] - Radius of Horn Profile at [L] = 0 ...{18}

For

[Rl] - OS-Horn Radius at Profile Length [L]

= {([Mc]^2)*([L]^2)+([Ro]^2)}^(1/2) ...[05]

Characterize [Ro] in Terms of [Rt], [Lt] & [Mc]

[Rt] = {([Mc]^2)*([Lt]^2)+[Ro]^2}^(1/2) ...[06]

[Rt]^2 = ([Mc]^2)*([Lt]^2)+[Ro]^2 ...[07]

[Ro]^2 = -([Mc]^2)*([Lt]^2)+[Rt]^2 ...[08]

Characterize [Ro] in Terms of [Mt] & [Lt] & [Mc]

[Mt] = (([Mc]^2)*[Lt])/((([Mc]^2)*([Lt]^2)+([Ro]^2))^(1/2)) ...[09]

[Mt]^2 = (([Mc]^4)*[LT]^2)/(([Mc]^2)*([Lt]^2)+[Ro]^2) ...[10]

([MC]^2)*([LT]^2)+([Ro]^2) = (([Mc]^4)/([Mt]^2))*([LT]^2) ...[11]

([Ro]^2) = ((([Mc]^4)/([Mt]^2))-([MC]^2))*([LT]^2) ...[12]

From [08] & [12] Solve for [Lt]

([Mc]^4)/([Mt]^2))*([Lt]^2)=[RT]^2 ...[13]

[Lt]^2 = ([Rt]^2)*([Mt]^2)/([Mc]^4) ...[14]

[Lt] = {([Rt]^2)*([Mt]^2)/([Mc]^4)}^(1/2) ...[15]

From [08] & [14] Solve for [Ro]

[Ro]^2 = -([Mc]^2)*([Rt]^2)*([Mt]^2)/([Mc]^4)+([Rt]^2) ...[16]

[Ro]^2 = ([Rt]^2)*(1-([Mt]^2)/([Mc]^2)) ...[17]

[Ro] = [Rt]*{(1-([Mt]^2))/([Mc]^2)}^(1/2) ...[18]