How to calculate distance and time?

I have sets of data for schedule based airline flights. at t1, t2, t3...., I have corresponding velocities, v1, v2,v3... etc. I have another set of different speeds, such as s1, s2, s3 .... My main objective is to find the time l1, where the aircraft travels the distance of the first set of data with the speeds of s1, s2, s3.... (Note: These speeds correspond to t1, t2, t3 as well.)

Anyone have any idea to do this? Any idea will be appreciated. Thanks.

[Star Strider]

What is the difference between ‘velocity’ and ‘speed’? How do they relate?

Are the ‘speed’ data the speeds of each leg of a particular flight? Something else?

[bio lim]

I am very sorry as in my description the speed and the velocity data are exactly same. (Both are speed).

Answer 1

[Walter Roberson]

You do not have a distance for the first set of data.

If you know any two of duration, speed, and distance, then you can find the third. But you do not have duration, you have desired times of take-off. You do have speeds: you have two sets of speeds that we do not know how to distinguish, the v-series and the s-series. You do not have distances.

Airline scheduling usually involves nodes (cities) and edges (direct flight connections with known ground distances) and collections of aircraft with individual known maximum cruising air velocities. In the simple case, winds are ignored completely. In a slightly more advanced case, the edges are no longer considered bidirectional and instead different unidirectional "distances" are assigned in the two directions. In a more advanced case, winds act as non-linear friction. In a step up after that, winds are modeled as being different in different geographic regions, modeled by introducing a whole series of connected intermediate nodes and running a shortest-path algorithm to determine the best route to get between distinguished nodes (the cities); this also allows one to model there being different speeds for take-off and for landing and for cruising. And then you get into market capacity demands, and per-aircraft capacity limitations. And calculating fuel requirements based upon weight where the weight lowers as the flight progresses. And connecting flights (which are important because individual travelers have different destinations but it is not economical to fly directly between all possible destinations.)

With just start times and velocities, you do not have any kind of scheduling task: you just have a bunch of straight line plots about "how far will they have traveled if they kept flying indefinitely?" Not traveled for any particular purpose, or from any particular location, just a whole bunch of (speed * current duration) plots with different t offsets. Like

%arbitrarily assume mapping up to 10 hours and 50 subdivisions for mapping

delta_t = linspace(0, 10, 50);  %row vector!

start_times = t;   %the given values
velocities = v;    %the given values

end_times = [ones(length(start_times),1), start_times(:)] * [delta_t; ones(1,length(delta_t))]   %matrix multiply intended
how_far_traveled = velocities(:) * delta_t;  %matrix multiply intended

plot(end_times', how_far_traveled');

[bio lim]

I am very sorry for my uninformative description, as I didn't want to go into full details. The data I am currently using are real-time data obtained from a research center. The speed vector, [v1, v2.....] is in fact the ground speed derived from the displacement using the position of the aircraft, and the flight time. The Indicated Airpseed was given as [s1, s2...]. Assuming that the aircraft travelled with v1 for t2-t1, I thought that I would be able to find the specific distance at that moment. What I am trying to find is the flight time if the aircraft was travelling with its Indicated Airpseed.

[Walter Roberson]

I am not sure but I think you might need the altitude information; see http://www.airliners.net/aviation-forums/tech_ops/read.main/45537/. Or alternately, if the groundspeed and IAS are known I think that might allow you to calculate your altitude. But if you already know the groundspeed and the ground distance to travel, then isn't the flight time just the simple ground distance divided by ground speed?

[Star Strider]

Actually, you need the density altitude (air density corrected for pressure altitude and temperature, but expressed in terms of the International Standard Altitude) to get true airspeed (TAS). Ground speed (GS) is the net result of wind velocity and direction at altitude, incorporating its headwind and crosswind components, and TAS. Groundspeed and distance (course) are all you need to calculate flight time, but fuel consumption is a function of the course, pressure altitude, TAS, and winds (that determine heading). Indicated airpseed (IAS) is usually chosen to be the airspeed at which the airplane has the most efficient fuel consumption, and is generally at the pilot’s discretion, although en route air traffic control can request a pilot to maintain a specific airspeed to guarantee optimal separation. Departure and approach control enforce much lower airspeeds (usually below 250 kts), but this is a relatively small fraction of total flight time.