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Dave,

How about Modern Haversine Sight Reduction (MHSR) ?

The original formula can be refered to as Classic Doniol Sight Reduction (CDSR).

Classic Doniol is a very good sight reduction method but requires a pair of tables and a rule for when the latitude declination sum is greater than 90°. It is the classic Doniol method that I have posted in my sailing blog. The MHSR uses only a single compact table with no special rules which makes it a better sight reduction method.

http://gregrudzinski.blogspot.com/2014/06/longhand-sight-reduction.html

Greg Rudzinski

From: David Fleming
Date: 2015 May 18, 15:38 -0700

I have given my Navigation students the formula hav(Zd) = n+(1-n-p)hav(t) as the preferred calculator backup method along with 4 place hav tables and a Rust azimuth diagram.

Because the solution requires

a) 4 in head additions - {eg 45d 18m - 10d25m} 

b) 4 table lookups - haversine table

c) 2 additions - ( eg abcd + efgh) this strikes me as harder than case a)

d) and one 4 digit x 4 digit multiply

e) plus Rust diagram

The haversine table is really small ( but to my old eyes Hanno has made it factor of 2 too small.)

P.S.  I think the name for this needs to be distinct from Doniol.