McKibben - Martindale - Hawkindale - Bartok

After talking to Ed Levin at the TFG Conference in Burlington Vermont about Rees Hawkins Acheson developing the Timber Framing Hawkindale angles,  I  thought I would write this article showing who knew what at each period in time. I'm guessing with more information being published on the web each day we'll probably be able to trace the Roof Framing Ratios Angle Formulas back to the year 1850 or so when builders started using steel for the rafters.


 The Hawkindale angles (1987) were based on the book by Frank L. Martindale "Bevel Angles for Three Dimensional Connections" 1948 that was based on the book "Hip and Valley Design" by H. L. McKibben and L. E. Gray published in 1912. The real difference in the three sets of Roof Framing Ratios Angle Formulas are the angles R4, R5, R6, R7, P4, P5, P6, C3,C4 developed by Rees Hawkins Acheson that only pertain to hip rafter purlin housing connections and seat angles. There are no hip rafter purlin housing connections for the steel purlin webs. Joe Bartok should also be included in this list of mathematicians. Joe developed another 10 or so Roof Framing Ratios Angle Formulas that pertain to the hip rafter purlin housing connections and seat angles.


McKibben --1912
 S = 33.6900700000°
 D = 45.0000000000°
 R1 = 25.2394038881°
 L1 = 29.0171421988°
 L2 = 39.7621583409°
 L3 = 18.0744554457°
 L4 = 37.4295371560°
 L5 = 36.0398922302°
 L6 = 14.5291550426°
 L7 = 18.1479754296°
 L8 = 39.7621583409°
 L9 = 23.0934708522°
 L10 = 23.0934708522°
 L11 = 47.8695857235°

 Martindale -- 1948
 S = 33.6900700000°
 D = 45.0000000000°
 R1 = 25.2394038881°
 R2 = 18.0744554457°
 R3 = 37.4295371560°
 P1 = 29.0171421988°
 P2 = 39.7621583409°
 P3 = 18.1479754296°
 C1 = 17.9202155395°
 C2 = 14.5291550426°
 C3 = 39.7621583409°
 C4 = 36.0398922302°
 C5 = 23.0934708522°
 C6 = 66.9065291478°

 Hawkindale -- 1987
 S = 33.6900700000°
 D = 45.0000000000°
 R1 = 25.2394038881°
 R2 = 18.0744554457°
 R3 = 37.4295371560°
 R4 = 42.1304142765°
 R5 = 18.4349504310°
 R6 = -80.4613223122°
 R7 = 31.2906189866°
 P1 = 29.0171421988°
 P2 = 39.7621583409°
 P3 = 18.1479754296°
 P4 = 32.4675251209°
 P5 = 39.7621583409°
 P6 = 15.2551195690°
 C1 = 36.0398922302°
 C2 = 14.5291550426°
 C3 = 23.0934708522°
 C4 = 39.7621583409°
 C5 = 23.0934708522°
 A5 = 17.5484020007°
 A7 = 25.2394038881°
 A8 = 7.2946332200°
 A9 = 10.4756833182°