Formula to Calculate ideal subject height

https://www.scantips.com/lights/subjectdistance.html

Real Object height * = Distance to Object * × Object height on sensor (mm)/Focal Length (mm)

d = 10 # feet
FFsensorHeightmm = 23.9 # mm
f = 200 # mm

Assume you want to fill 70% of sensor height.

Real target object height =

rh<- d*0.7*FFsensorHeightmm/f
rh * 12  # convert feet to inches
## [1] 10.038

Any real target less than 10 inches will fill less than 70% of sensor height at 10’ distance.

DOF

https://en.wikipedia.org/wiki/Depth_of_field

https://en.wikipedia.org/wiki/Zeiss_formula

DOF approx = 2d^2 * fNum * c/f^2

c = ((FFsensorHeightmm^2 + FFsensorWidthmm2)0.5)/1500

FFsensorWidthmm = 35.9 # mm
c = ((FFsensorHeightmm^2 + FFsensorWidthmm^2)^0.5)/1500
c
## [1] 0.02875197
# Using above example with fNum = 5.6
fNum= 5.6
DOF = (2*(d*304.8)^2 * fNum * c)/f^2
DOF * 0.0393701
## [1] 2.944571

Result roughly agrees with result from https://dofsimulator.net/en/ 2.9" vs 2.8" correct answer.

Tables

For a given real object (e.g., warbler), you can rearrange formulas to calculate zoom for a given distance and a desired fill of the vertical sensor height. Assuming a reasonable DOF for that target, you can calculate the fNumber as well (which is constant for a specific target and sensor fill).

Warbler 3" bird height, 1" DOF

ans # fill 70% of sensor height
##      dist   zoom     fNum
## [1,]    5  334.6 21.29208
## [2,]   10  669.2 21.29208
## [3,]   20 1338.4 21.29208
## [4,]   50 3346.0 21.29208
ans # fill 50% of sensor height
##      dist zoom     fNum
## [1,]    5  239 10.86331
## [2,]   10  478 10.86331
## [3,]   20  956 10.86331
## [4,]   50 2390 10.86331
ans # fill 33% of sensor height
##      dist    zoom     fNum
## [1,]    5  157.74 4.732056
## [2,]   10  315.48 4.732056
## [3,]   20  630.96 4.732056
## [4,]   50 1577.40 4.732056

Blue Jay 6" bird height, 3" DOF

ans # fill 70% of sensor height
##      dist   zoom     fNum
## [1,]    5  167.3 15.96906
## [2,]   10  334.6 15.96906
## [3,]   20  669.2 15.96906
## [4,]   50 1673.0 15.96906
ans # fill 50% of sensor height
##      dist   zoom    fNum
## [1,]    5  119.5 8.14748
## [2,]   10  239.0 8.14748
## [3,]   20  478.0 8.14748
## [4,]   50 1195.0 8.14748
ans # fill 33% of sensor height
##      dist   zoom     fNum
## [1,]    5  78.87 3.549042
## [2,]   10 157.74 3.549042
## [3,]   20 315.48 3.549042
## [4,]   50 788.70 3.549042

Duck? 12" bird height, 6" DOF

ans # fill 70% of sensor height
##      dist   zoom    fNum
## [1,]    5  83.65 7.98453
## [2,]   10 167.30 7.98453
## [3,]   20 334.60 7.98453
## [4,]   50 836.50 7.98453
ans # fill 50% of sensor height
##      dist   zoom    fNum
## [1,]    5  59.75 4.07374
## [2,]   10 119.50 4.07374
## [3,]   20 239.00 4.07374
## [4,]   50 597.50 4.07374
ans # fill 33% of sensor height
##      dist    zoom     fNum
## [1,]    5  39.435 1.774521
## [2,]   10  78.870 1.774521
## [3,]   20 157.740 1.774521
## [4,]   50 394.350 1.774521

Penguin 25" bird height, 7" DOF

ans # fill 70% of sensor height
##      dist    zoom     fNum
## [1,]    5  40.152 2.146242
## [2,]   10  80.304 2.146242
## [3,]   20 160.608 2.146242
## [4,]   50 401.520 2.146242
ans # fill 50% of sensor height
##      dist   zoom     fNum
## [1,]    5  28.68 1.095021
## [2,]   10  57.36 1.095021
## [3,]   20 114.72 1.095021
## [4,]   50 286.80 1.095021
ans # fill 33% of sensor height
##      dist     zoom      fNum
## [1,]    5  18.9288 0.4769913
## [2,]   10  37.8576 0.4769913
## [3,]   20  75.7152 0.4769913
## [4,]   50 189.2880 0.4769913