BoulderHyattHopper - Try this:
When I was in high school (which was shortly after they invented dirt), there was a typical math word problem somewhat as follows: A powered boat goes at a rate of "S" miles per hour in still water. How far does it travel (i.e., what is the
net speed) if going upstream or downstream when the current is "C" miles per hour?
The answer was, if going downstream, add the current to the speed ("S"+"C" mph); if going upstream subtract the current from the speed ("S"-"C" mph).
You can use that concept to make a simple formula for the problem:
1. Take the speed of the plane (in miles per hour), subtract the headwind (in miles per hour) and you have the number of miles the plane actually travels in an hour.
2. Divide the total miles to Hawaii by that number. This gives you the number of hours it will take to get to Hawaii.
3. Divide that number by 2. This gives you the number of hours it takes to get half-way to Hawaii.
4. Convert that number (which will be a decimal) into hours/minutes/seconds.
5. Add the resulting number to the time of take-off.
And there you have the answer (if they're asking what time it will be at the take-off point when you pass the "half-way to Hawaii" point, which is what they used to ask).
I've used this formula on the "half-way to Hawaii" with reasonable success.
The formula is simple, but also simplistic. It does not take into consideration that the headwind or tailwind is not blowing along the axis of flight (i.e., you're not flying directly into the wind, or directly in front of the wind), and thus shouldn't be adding or subtracting the whole speed of the wind (rather the wind causes a vector; if you want to figure it out, make a triangle with one leg being the speed of the plane, another being the speed of the wind, and the angle between them being the angle at which the wind is blowing on the plane; since "side-angle-side" determines a unique triangle, the third leg of the triangle becomes the distance covered per unit of time). It also doesn't take into consideration variations in speed of the wind, or of the plane as it becomes lighter through consumption of fuel. And there are a lot of other factors that it doesn’t take into consideration, including
Glen’s Champagne.
But then again, that would take all the fun out of it.
(Edited to add more explanation.)
[This message has been edited by Counsellor (edited 09-26-2002).]