Hi,
Unfortunately you have some inconsistent data in your question, but
never the less you have provided ample information to have the
question answered. The formula is relatively simple; the pilot has
done the hard bit for you and given you the head wind speed, airspeed
and distance. In a real situation the wind never blows directly
towards the plane so you invariably have to calculate a crosswind and
headwind component of the wind which will affect both distance
travelled and relative ground speed.
Your question states the halfway point in miles between Los Angeles
and Honolulu as being 2221 miles. This is not correct (unless you are
going via Alaska). The distance between these 2 cities is
approximately 2560 miles.
http://www.javacommerce.com/cooljava/calculators/airdistance.html
This will vary given the crosswind value as described above. From this
we can begin to form an equation. Unfortuantly all the maths must be
done here as I have nowhere to host an Excel spreadsheet file for you.
It is just a matter of plugging these values into a spreadsheet
though.
A1 = Distance to Geographical “halfway” (miles)
A2 = AirSpeed (knots (First Half))
A3 = Head/Tail Wind (knots – make this positive for tailwind, negative
for head wind)
A4 = Conversion from Knots to mph (=1.15077945)
A5 = Departure Time (hh:mm)
A6 = A2 + A3 (GroundSpeed in knots)
A7 = A6 * A4 (Ground Speed in mph)
A8 = TEXT((A1/A7)/24,"hh:mm:ss" ) (Time taken in hh:mm:ss)
A9 = A5 + A8 (Arrival time at geographical halfway = Answer)
So plugging in your values (given total distance is 2560 miles, not
4442 miles):
(488 +(– 24))*1.15077945) * (2560/2) = 2.39 hours = 2 hours 23 minutes
50 seconds
Adding this value to your departure time of 13:48:00, we get 16:11:50
– pretty close to your correct answer of 16:14:25. The discrepancy
here is to do with the distance given (which will have been adjusted
to accommodate crosswinds). Adjusting the distance for crosswinds by
23 miles for the first half of the journey (which is well within
reasonable bounds) gives the correct answer of 16:14:25.
If you can provide the correct distance you were given we can double
check the formula to make sure it works. If it turns out you are given
the distance in knots rather than miles per hour, simple make the
value of cell A4 = 1.
Enjoy the Champagne!
Molloch |
Clarification of Answer by
molloch-ga
on
17 Jun 2002 04:01 PDT
Thanks.
Did the pilot give you the crosswind factor or did he give the head
wind speed as a factor? The way to work out the headwind and deviation
given a crosswind is quite complex, it involves calculating a
head/tail wind force and a perpendicular force on the aircraft from a
the angle the wind is hitting the plane. I doubt they would give you
that information as the equation would be quite complex. Imagine that
the distance/velocity is affected in a crosswind as relative to the
air, the plane is flying on an angle to compensate for the wind.
I'll just elaborate on the formula a little so you can adapt it if
necessary, I'll explain it in a bit more depth for you (was late for
work before!):
Firstly you have to calculate a ground speed. The airspeed given is
the speed at which the air is passing the plane, this speed will be
effected by the head/tail wind. If there is a headwind you will need
to subtract the headwind speed from the airspeed, if a tailwind you
will need to add the tailwind speed to the airspeed. This is because
the airspeed of the plane is relative to the airspeed. Imagine you are
in a train travelling at 100 mph and run from the back end of the
train to the front at 5 mph. You are travelling at 5 mph compared to
the train but 105 mph compared to the ground (ground speed). If you
ran from front to back you would be travelling at 95mph groundspeed,
but still 5mph compared to the train. Now you have the relative ground
speed.
If the distance is in Nautical miles, you need to convert to miles by
multiplying it by the conversion factor: 1.15077945, there are this
many miles in each nautical mile.
From this you can work out the time taken in hours (in decimal form),
Excel converts this to minutes/seconds with the function
TEXT(value/24, "hh:mm:ss") where value is the decimal value calculated
before. You divide by 24 to get the "time past midnight" which is the
format Excel works in.
Adding this value to the departure time gives you your answer.
I'm happy to answer any more questions if you have them and can point
you to some websites that show calculations involving crosswinds etc.
Beware that this can get extremely confusing!
Hope this is helpful
Molloch
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