2004 11 24
Analysis of height error due solely to angle measurement error using the sine*distance (ENTS) method.
Scenario:  You are at a fixed distance from a tree.  (DB)  You accurately measure the distance to the top.  (DT)
You measure the angle to the top, or any other point on the tree, but there is an error in your measurement (e).
Since we are focusing on angle error, we assume the tree is vertical.  The only difference would be a change in the baseline.  The "error as a percent of baseline" is still the same.
DB is the true horizontal distance to the point directly beneath the top.
DT is the true distance to the top.
a is the true angle to the top.
e is the angle measurement error.
H is the true height.
H' is the height calculated using the erroneous angle measurement.
Facts:  DT = DB/cos(a);  H = DT*sin(a);  H' = DT*sin(a+e)
Formula used:  H-H' = DT*sin(a) - DT*sin(a+e) = (DB/cos(a))*(sin(a)-sin(a+e))
My conclusion:  At a given baseline, the height error due to angle measurement error is nearly the same no matter what the angle.
Also, at 50 yards horizontal, the height error due to a 0.4 degree clinometer error is about 1 foot.
Enter the angle error in b6.  Enter the baseline distance to the tree in b7.
angle error (degrees)>>	0.4	e
true baseline distance to point below top (yards)>>	50	DB
Here are a series of angles and the height error that results
	a	a+e	DT	H	H'	H-H'	(H-H')/H
	true angle	true angle + error	(yards)	true height (feet)	calc height (feet)	height error (feet)	hgt error percent of baseline			(sin(a)-sin(a+e))/cos(a)
	-10	-9.6	50.77	-26.45	-25.40	-1.0478	-0.70%			-0.0070
	-5	-4.6	50.19	-13.12	-12.08	-1.0475	-0.70%			-0.0070
	0	0.4	50.00	0.00	1.05	-1.0472	-0.70%			-0.0070
	5	5.4	50.19	13.12	14.17	-1.0469	-0.70%			-0.0070
	10	10.4	50.77	26.45	27.50	-1.0465	-0.70%			-0.0070
	15	15.4	51.76	40.19	41.24	-1.0462	-0.70%			-0.0070
	20	20.4	53.21	54.60	55.64	-1.0459	-0.70%			-0.0070
	25	25.4	55.17	69.95	70.99	-1.0455	-0.70%			-0.0070
	30	30.4	57.74	86.60	87.65	-1.0451	-0.70%			-0.0070
	35	35.4	61.04	105.03	106.08	-1.0446	-0.70%			-0.0070
	40	40.4	65.27	125.86	126.91	-1.0441	-0.70%			-0.0070
	45	45.4	70.71	150.00	151.04	-1.0435	-0.70%			-0.0070
	50	50.4	77.79	178.76	179.81	-1.0428	-0.70%			-0.0070
	55	55.4	87.17	214.22	215.26	-1.0420	-0.69%			-0.0069
	60	60.4	100.00	259.81	260.85	-1.0409	-0.69%			-0.0069
	65	65.4	118.31	321.68	322.72	-1.0394	-0.69%			-0.0069
	70	70.4	146.19	412.12	413.16	-1.0371	-0.69%			-0.0069
	75	75.4	193.19	559.81	560.84	-1.0335	-0.69%			-0.0069
	80	80.4	287.94	850.69	851.72	-1.0265	-0.68%			-0.0068
	85	85.4	573.69	1714.51	1715.51	-1.0054	-0.67%			-0.0067
	90	90.4	########	##############	##############	##############	#########			########