In a recent weekend sail the discussion revolved around how to figure out where the true wind was coming from and its speed, given information on the speed and direction of the apparent wind and the speed of the boat. It seems reletively easy to calculate if the true wind is on the nose or from astern but trying to come up with a formula that covers all of the point in between got complicated. Does anyone know the formula, or where to obtain tables, or can help figure this out. Thanks.Eric
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Vectors
Hi Eric, Well here's a partial answer. Hopefully you'll remember vectors from high school or college math or physics. The apparent wind is a vector that combines the force and angle of the true wind, with the wind force and angle created by the boat's movement. If you know the these two forces and angles, you can calculate the true wind using trigonometry. Let's see... the sine of angle A divided by the wind force multiplied by the tangent of angle B... hmm that was about 35 years ago and I seem to have forgotten a bit. Either that or you can push the true/apparent toggle switch on your wind indicator. As I said, a partial answer. Maybe there's an engineer or a mathematician out there that can provide the rest. Gary Wyngarden S/V Wanderlust H37.5
Hi Eric, Well here's a partial answer. Hopefully you'll remember vectors from high school or college math or physics. The apparent wind is a vector that combines the force and angle of the true wind, with the wind force and angle created by the boat's movement. If you know the these two forces and angles, you can calculate the true wind using trigonometry. Let's see... the sine of angle A divided by the wind force multiplied by the tangent of angle B... hmm that was about 35 years ago and I seem to have forgotten a bit. Either that or you can push the true/apparent toggle switch on your wind indicator. As I said, a partial answer. Maybe there's an engineer or a mathematician out there that can provide the rest. Gary Wyngarden S/V Wanderlust H37.5
Draw Arrows (Vectors)
Get some quarter inch graph paper. Draw an arrow straight up as long as your boat speed (GPS is best.) Use 5 knots as an example, so the arrow is 5 squares long. Draw a second arrow starting at the point of the boat speed arrow representing the apparent wind. Say the apparent wind is 10 knots, at 60 degrees off your starboard bow. So the apparent wind arrow is 10 quarters of an inch long (2 1/2 inches. It starts at the point of the boat speed arrow and goes to the left, down at angle of 60 degrees to the boat speed arrow. The true wind arrow starts at the bottom of the boat speed arrow, and ends at the point of the apparent wind arrow. If you drew the first two arrows correctly, the true wind arrow is about 8 and 2/3 squares long, and it points straight (90 degrees) left. So the true wind is about 8 2/3 knots, and is blowing 90 degrees off the starboard bow. If you play around drawing arrows for different speeds, you will soon develop an intuitive feel for the relationship. Yes, there is a formula, but I like the arrows (or vectors) better, and they are actually the best model for the problem. Yes, I did choose a special triangle for the example. All engineering test questions seem to use the triangle with the short leg of 1, the long 60 degree leg of 2, and the leg at right (90 degrees) angle from the start of the short side is the square root of 3. (About 1.73 times 5 is 8.65, or about 8 2/3.) David Lady Lillie
Get some quarter inch graph paper. Draw an arrow straight up as long as your boat speed (GPS is best.) Use 5 knots as an example, so the arrow is 5 squares long. Draw a second arrow starting at the point of the boat speed arrow representing the apparent wind. Say the apparent wind is 10 knots, at 60 degrees off your starboard bow. So the apparent wind arrow is 10 quarters of an inch long (2 1/2 inches. It starts at the point of the boat speed arrow and goes to the left, down at angle of 60 degrees to the boat speed arrow. The true wind arrow starts at the bottom of the boat speed arrow, and ends at the point of the apparent wind arrow. If you drew the first two arrows correctly, the true wind arrow is about 8 and 2/3 squares long, and it points straight (90 degrees) left. So the true wind is about 8 2/3 knots, and is blowing 90 degrees off the starboard bow. If you play around drawing arrows for different speeds, you will soon develop an intuitive feel for the relationship. Yes, there is a formula, but I like the arrows (or vectors) better, and they are actually the best model for the problem. Yes, I did choose a special triangle for the example. All engineering test questions seem to use the triangle with the short leg of 1, the long 60 degree leg of 2, and the leg at right (90 degrees) angle from the start of the short side is the square root of 3. (About 1.73 times 5 is 8.65, or about 8 2/3.) David Lady Lillie
Ask a Pilot
Entice him with a beer or two or three. It may take a six pack to get through it though. He will even show you his handy EA6B that does all the figuring it will not be marked for speeds as low as we use but try using 60 for 6 100 for 10 and so on then divide by ten. I am sure the is a spreadsheet out there that would do the same thing maybe one that you can use on your palm.
Entice him with a beer or two or three. It may take a six pack to get through it though. He will even show you his handy EA6B that does all the figuring it will not be marked for speeds as low as we use but try using 60 for 6 100 for 10 and so on then divide by ten. I am sure the is a spreadsheet out there that would do the same thing maybe one that you can use on your palm.
Simple Vector Equation...
...if you have a calculator that does calculations using polar coordinates. The equation using polar coordinates is: True Wind Vector (Wind Speed, Angle off the bow) = Apparent Wind Vector (Wind Speed, Angle off the bow) - Boat Speed Vector (Boat Speed,0 degrees). The Boat Speed Vector is the boat speed in knots with 0 degrees angle off the bow. The Apparent Wind Vector is the wind speed the boat is measuring in knots and the wind angle measured off the bow. The trigonometric equation is: True Wind Speed = [{Apparent Wind Speed x cosine (90 - Apparent Wind Angle)}^2 + {Apparent Wind Speed x sine (90 - Apparent Wind Angle) - Boat Speed}^2]^1/2 True Wind Angle off the bow = Arctangent [Apparent Wind Speed x sine (90 - Apparent Wind Angle) - Boat Speed / Apparent Wind Speed x cosine ( 90 - Apparent Wind Angle)] I have a calculator that does math using polar coordinates, so it's easy for me to do the math, I just plug in the two vectors in polar coordinates and hit the minus button. If you don't have a scientific calculator that does math using polar coordinates or sine, cosine and arctangent functions, then you can use the online calculator on US Sailing's website. Fair Winds, Clyde
...if you have a calculator that does calculations using polar coordinates. The equation using polar coordinates is: True Wind Vector (Wind Speed, Angle off the bow) = Apparent Wind Vector (Wind Speed, Angle off the bow) - Boat Speed Vector (Boat Speed,0 degrees). The Boat Speed Vector is the boat speed in knots with 0 degrees angle off the bow. The Apparent Wind Vector is the wind speed the boat is measuring in knots and the wind angle measured off the bow. The trigonometric equation is: True Wind Speed = [{Apparent Wind Speed x cosine (90 - Apparent Wind Angle)}^2 + {Apparent Wind Speed x sine (90 - Apparent Wind Angle) - Boat Speed}^2]^1/2 True Wind Angle off the bow = Arctangent [Apparent Wind Speed x sine (90 - Apparent Wind Angle) - Boat Speed / Apparent Wind Speed x cosine ( 90 - Apparent Wind Angle)] I have a calculator that does math using polar coordinates, so it's easy for me to do the math, I just plug in the two vectors in polar coordinates and hit the minus button. If you don't have a scientific calculator that does math using polar coordinates or sine, cosine and arctangent functions, then you can use the online calculator on US Sailing's website. Fair Winds, Clyde
Buy an E6B
You can pick up and inexpensive E6B from WWW.Sportys.COM It is nothing more than a circular slide rule, with a whiz wheel on the back for the vector equations. Onnce you get used to it, you can plot quite accurately true and apparent wind and speeds, and caluclate course,drift, fuel consumption,ETA, and a myriad of other very useful calculations. Not bad for around $20 !!
You can pick up and inexpensive E6B from WWW.Sportys.COM It is nothing more than a circular slide rule, with a whiz wheel on the back for the vector equations. Onnce you get used to it, you can plot quite accurately true and apparent wind and speeds, and caluclate course,drift, fuel consumption,ETA, and a myriad of other very useful calculations. Not bad for around $20 !!
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