Ruth's Waterfalls

Ruth's Waterfalls
of the Finger Lakes, Rochester, and Ithaca, NY.

How High?

When we first started visiting waterfall gullies, it seemed like some of the waterfalls were hundreds of feet high. Others, which didn't seem like much at first turned out to be thirty footers (respectable waterfalls in these parts). Then we discovered the Waterfalls of Western New York survey and learned from Scott that it is fun to accurately measure the height rather than just guessing. We learned the technique from Scott and from his website and have since acquired our own clinometer, rangefinder, and notebook. So here we go.

Overview
How to measure
Example
Estimating table
Gravity method

Waterfall Height Calculator

Excel 97 Height Calculator

Overview

The technique involves measuring the angle of a line of sight to the top or bottom of the waterfall and then the distance along that line of sight. Then, struggling to remember our high school trigonometry, we multiply the distance times the sine of the angle to get the height of the opposite side of the triangle. Normally, we make a note of the angle and the distance and wait until we get home to use a pocket calculator or computer to perform the calculation.

We have a Waterfall Height Calculator you can use to perform the calculations. We also have an Excel 97 spreadsheet you can use to do the same thing; download it by clicking here. Instructions are included in the spreadsheet. We use it on a Windows PC, but you might get it to work on a Mac.

How to measure (Top)

You can measure from the bottom or top of the waterfall. Stand with your feet even with the plunge pool or the crest of the waterfall.


When measuring from the bottom up, calculate the height and then add the distance from the plunge pool to your eyes.	When measuring from the top down, calculate the height and then subtract the distance from your eyes to the crest of the waterfall.

If you can't get to the top or bottom of the waterfall, you can still measure the height by taking two sightings.


If you are standing opposite the waterfall, take two sightings and then add the height calculations together.	If you are standing below the plunge pool, take one sighting to the crest and a second sighting to the plunge pool. Subtract the second height from the first.	If you are standing opposite the waterfall and looking down on it, take one sighting to the plunge pool and a second sighting to the crest. Subtract the second height from the first.

Example (Top)

Here is an example. You stand at the crest of the waterfall and sight to a stone on the far side of the plunge pool. With your clinometer, you measure the angle of the line of sight to be 38 degrees from horizontal. With your range finder, you measure the distance to the stone as 57 feet. You look in the table below in the 40 degree column and the 55 foot row to find the estimated height of 35.4 feet. Since you are standing at the top, you need to subtract the distance from your feet to your eyes, about 5.5 feet and you get an estimated height of the waterfall as 35.4 minus 5.5, or 30 feet. Later, you run the numbers through the Excel spreadsheet or the Waterfall Height Calculator and find that the actual height is 29.6 feet.

Estimating Table (Top)

You can use the table below to get a pretty good estimate of the height if you know the angle and distance. Find the closest angle in the row at the top of the table and the nearest distance in the column at the left and then lookup the height. If you are sighting from the bottom up, you need to add the distance from your eyes to your feet; if you are sighting from the top down, subtract.

	20°	25°	30°	35°	40°	45°	50°	55°	60°
25	8.6	10.6	12.5	14.3	16.1	17.7	19.2	20.5	21.7
30	10.3	12.7	15.0	17.2	19.3	21.2	23.0	24.6	26.0
35	12.0	14.8	17.5	20.1	22.5	24.7	26.8	28.7	30.3
40	13.7	16.9	20.0	22.9	25.7	28.3	30.6	32.8	34.6
45	15.4	19.0	22.5	25.8	28.9	31.8	34.5	36.9	39.0
50	17.1	21.1	25.0	28.7	32.1	35.4	38.3	41.0	43.3
55	18.8	23.2	27.5	31.5	35.4	38.9	42.1	45.1	47.6
60	20.5	25.4	30.0	34.4	38.6	42.4	46.0	49.1	52.0
65	22.2	27.5	32.5	37.3	41.8	46.0	49.8	53.2	56.3
70	23.9	29.6	35.0	40.2	45.0	49.5	53.6	57.3	60.6
75	25.7	31.7	37.5	43.0	48.2	53.0	57.5	61.4	65.0
80	27.4	33.8	40.0	45.9	51.4	56.6	61.3	65.5	69.3
85	29.1	35.9	42.5	48.8	54.6	60.1	65.1	69.6	73.6
90	30.8	38.0	45.0	51.6	57.9	63.6	68.9	73.7	77.9
95	32.5	40.1	47.5	54.5	61.1	67.2	72.8	77.8	82.3
100	34.2	42.3	50.0	57.4	64.3	70.7	76.6	81.9	86.6
105	35.9	44.4	52.5	60.2	67.5	74.2	80.4	86.0	90.9
110	37.6	46.5	55.0	63.1	70.7	77.8	84.3	90.1	95.3
115	39.3	48.6	57.5	66.0	73.9	81.3	88.1	94.2	99.6
120	41.0	50.7	60.0	68.8	77.1	84.9	91.9	98.3	103.9
125	42.8	52.8	62.5	71.7	80.3	88.4	95.8	102.4	108.3
130	44.5	54.9	65.0	74.6	83.6	91.9	99.6	106.5	112.6
135	46.2	57.1	67.5	77.4	86.8	95.5	103.4	110.6	116.9
140	47.9	59.2	70.0	80.3	90.0	99.0	107.2	114.7	121.2
145	49.6	61.3	72.5	83.2	93.2	102.5	111.1	118.8	125.6
150	51.3	63.4	75.0	86.0	96.4	106.1	114.9	122.9	129.9
155	53.0	65.5	77.5	88.9	99.6	109.6	118.7	127.0	134.2
160	54.7	67.6	80.0	91.8	102.8	113.1	122.6	131.1	138.6
165	56.4	69.7	82.5	94.6	106.1	116.7	126.4	135.2	142.9
170	58.1	71.8	85.0	97.5	109.3	120.2	130.2	139.3	147.2
175	59.9	74.0	87.5	100.4	112.5	123.7	134.1	143.4	151.6
180	61.6	76.1	90.0	103.2	115.7	127.3	137.9	147.4	155.9
185	63.3	78.2	92.5	106.1	118.9	130.8	141.7	151.5	160.2
190	65.0	80.3	95.0	109.0	122.1	134.4	145.5	155.6	164.5
195	66.7	82.4	97.5	111.8	125.3	137.9	149.4	159.7	168.9
200	68.4	84.5	100.0	114.7	128.6	141.4	153.2	163.8	173.2
205	70.1	86.6	102.5	117.6	131.8	145.0	157.0	167.9	177.5
210	71.8	88.7	105.0	120.5	135.0	148.5	160.9	172.0	181.9
215	73.5	90.9	107.5	123.3	138.2	152.0	164.7	176.1	186.2
220	75.2	93.0	110.0	126.2	141.4	155.6	168.5	180.2	190.5
225	77.0	95.1	112.5	129.1	144.6	159.1	172.4	184.3	194.9
230	78.7	97.2	115.0	131.9	147.8	162.6	176.2	188.4	199.2
235	80.4	99.3	117.5	134.8	151.1	166.2	180.0	192.5	203.5
240	82.1	101.4	120.0	137.7	154.3	169.7	183.9	196.6	207.8
245	83.8	103.5	122.5	140.5	157.5	173.2	187.7	200.7	212.2
250	85.5	105.7	125.0	143.4	160.7	176.8	191.5	204.8	216.5

Gravity method (Top)

Here is another way to measure the height, but it's not very accurate and it only works on high waterfalls. Throw a rock off the crest of the waterfall and see how long it takes to hit the plunge pool. You need a stop watch to measure the time. You need to throw the rock straight out in a horizontal direction. (Be careful that there are no hikers below you!) If your throw and timing are accurate, then you can estimate the height of the waterfall from the following table.

Time in Seconds	Distance in feet
1.00	16
1.25	25
1.50	36
1.75	49
2.00	64
2.25	81
2.50	100
2.75	121
3.00	144
3.25	169
3.50	196
3.75	225
4.00	256
4.25	289
4.50	324

Last modified: 10/09/2005