|Distance [nm.] × 60|
|Estimated Time En Route [Minutes] =||
|Ground Speed [kts.]|
First, the data needed:
There are two methods of calculating ETE, Estimated Time En Route. The first method is for the purists, or for those who have pulled their 747 out of the garage for a weekend flight and will be cruising at FL390.
Since this first flight is assumed in a zero-wind situation, the ground speed will be the same as the air speed, and the course heading is not a factor in the ground speed. Also, since the departure and destination field elevations are less than 100 ft., they will be ignored for ETE calculations, too.
Time to climb to cruise altitude = 4500 ft. / 700 fpm = 6.4 minutes or 0.11 hrs.
Distance covered during climb = 0.11 hrs. × 90 kts. = 10 nm.
Time to descend = 4500 ft. / 500 fpm = 9 minutes or 0.15 hrs.
Distance covered during descent = 0.15 hrs. × 110 kts. descent = 17 nm.
NOTE: Since we descend in the Nav Trainer at 110 kts, also the cruise speed, we wouldn't calculate descent time separately.
Balance of flight at cruise altitude = 54.5 nm. minus (10 nm. climb, + 17 nm. descent), = 27.5 nm. at cruise altitude.
Time at cruise altitude = 27.5 nm./110 kts. = 0.25 hrs., or 15 minutes.
Therefore, the ETE is:
|Time to climb||6 minutes|
|Time to descend||9 minutes|
|Time at cruise altitude||15 minutes|
ETE ... Method 2
D / TAS plus 5 minutes
Second method to calculate ETE: calculate the time to fly entire distance at cruise speed.
= 54.5 nm. / 110 kts. = 0.495 hrs. or 30 minutes.
Add 5 minutes for climb and descend. With this method, the calculated ETE is 35 minutes; 5 minutes longer than the "precise" calculation. For longer flights, this second method of calculation becomes more accurate.
At low cruising altitudes in VFR weather, the second method is very acceptable for calculating ETE.
The final calculation is the fuel consumption. The second method of calculating ETE will suffice for the time aloft to calculate fuel consumption. If you're piloting an airliner flying at high altitudes, as all airliners do, the fuel consumption should be calculated for climb in addition to cruise, as the climb fuel consumption rate is much higher than the cruise consumption rate.
ETE = (54.5 nm / 110 kts) + 0.083 (5 min. for climb and descent) = 0.58 hrs.
20 gph × 0.58 hrs = 11.6 gallons of fuel used for the flight.
Now click here to see the completed Flight Planning Worksheet for the first flight, New Bedford to Elizabeth Field.
Follow those ten steps for each leg of a flight.
Now let's fly the course!
Start the panel-mounted timer as you lift off from New Bedford's Runway 23 and stop it as you touchdown on Elizabeth Field's Runway 25. Compare your actual flight time against your calculations. You'll enjoy flying this aircraft with the oversize gauges.
Well, that was an interesting flight and mathematical exercise, but hardly one shrouded in realism. It was, though, a good stepping stone to handle the real-world issues of winds aloft, and their affect on navigating from point A to point B.
Winds aloft affect both the ground speed of the aircraft, and the heading that the aircraft must fly to stay on the desired true course.
Some pilots contend that a strong headwind is not a concern because the lost time will be gained on the return journey, when benefitting from the tailwind. The truth is, for a constant wind situation, the effects of a headwind cannot be reversed by the tailwind on the return trip. A simple calculation will end the discussion on this subject.
For illustration, assume a 180 nm. journey, a 60 kt. headwind, and an aircraft that cruises at 150 kts TAS.
The ground speed into the headwind will be 150 kts. minus 60 kts. wind or 90 kts. Time to fly the 180 nm. will be 180 nm. / 90 kts. ground speed, or 2.0 hrs.
For the return trip, ground speed will be 150 kts. plus 60 kts. tailwind, or 210 kts. Time to fly the return trip will be 180 nm. / 210 kts., or 0.86 hrs.
Total flight time with this wind situation = 2.0 hrs. + 0.86 hrs. = 2.86 hrs.
Now consider the no-wind journey. Still 180 nm. each way, total 360 nm. TAS of aircraft is 150 kts. Therefore total round-trip time, with no wind, will be 360 nm. / 150 kts. TAS, or 2.4 hours0.46 hrs. shorter than flying with the headwind and tailwind.
Try the calculation for any distances, any TAS, and any wind speed. The results remain the same. The effects of a headwind can not be overcome by the same tailwind.
"What did you do to Mr. Counter?" the Boss shouted. "He gave me an earful about your violent antics while landing at Fishers Island. Said your jerky maneuvers almost threw him out of the plane."
'Violent antics?' If I knew it would come to this I'd have barrel-rolled out.
"The deer that ran onto the runway as I was about to flare out left me with two choices," I replied, evenly. "It was either venison steaks ŕ la propeller blades at the expense of your sparkling-new Nav Trainer, or go around from a near-stall and put up with Counter’s complaintstough decision, but I chose the latter."
"He didn't mention a deer. Anyway, he’s giving us, you, one more chance, so don’t botch it. He needs to get from Lawrence Airport to Worcesterthis afternoon. His stock broker is in the Worcester office with a hot trade recommendation, but Counter wants to talk to him about it in person before the market closes.
"So give Counter a nice smooth flight and we might keep him as a customer," the Boss finished.
A nice smooth flight? A strong cold front had just raced through early this morning leaving very brisk north-westerly winds in its wake. Flying low and slow will be very bumpy.
Can't worry about that now. The flight originates at Lawrence, Mass., airport ID KLWM, then southwest to Worcester, airport ID KORH. Time to plot it and move on.
The illustration below shows the route of flight, which is still wholly contained on the New York sectional chart. A click on the image will download a zipped file of the same portion of this sectional for those without the chart. Go to the Downloads Section if you have a color printer.
Again, check the print-out of the sectional for faithfulness in size. The distance across two grid-squares should be 166 mm.
Print and begin a new Flight Planning Worksheet for this second flight. On the sectional plot the true course from Lawrence, Mass., KLWM, to Worcester, Mass., KORH.
Enter that information, along with the Worcester Airport, KORH. data onto the worksheet.
The winds aloft are 315° at 40 kts. That goes on the worksheet, too. Note, winds aloft commonly vary depending on altitude, but for this example they are considered constant regardless of altitude.
Now click here to see the Worksheet containing this initial data. If your results differ, recalculate or remeasure to find the problem. If your work is OK, and I messed up, please e-mail me and I'll correct whatever is wrong.
We draw a triangle on a sheet of paper to determine the wind correction angle (WCA) and ground speed (GS). It is a simple, six-step process that takes less time to do than to describe. Best of all, it's an approach that works whether the flight is simple or complex.
Begin by orienting the paper in the direction of the flight. For an east or west flight, the long side of the paper should be horizontal. For a north or south flight, turn the long side vertically. Use a separate sheet for each leg of the flight.
A conventional ruler or scale and a protractor will work fine for this work.
Now the steps of the wind triangle.
In summary, here are the steps to build a wind-triangle and then determine the aircraft's Ground Speed and Wind Correction Angle:
After you've drawn two or three wind triangles, you'll find you can complete the process in about 3 minutes.
Download the completed worksheet, flightplan-lwm1.pdf, from the Downloads Section.
Now climb into your Nav Trainer, with the Flight Sim weather set for a wind of 40 kts from 315°, note the headings, etc., in your Flight Planning Worksheet, and be on your way. Start the panel stopwatch as you roll down Lawrence Airport's Runway 33 and stop it after touchdown at Worcester. Compare your flight time with the predicted flight time.
Be sure to use the proper runway at Worcester. Land on Runway 33, not Runway 29. With this very strong wind, you could not keep the aircraft on the runway using any runway except 33.
And enjoy the flight. Give Ben Counter a nice ride.
While pencil, paper, ruler and protractor offer a simple, accurate, and quick method to calculate Ground Speed and Wind Correction Angles, more convenient devices have evolved over the years. Probably the most well known is the Dalton E6-B flight computer. The E6-B is basically a circular slide rule with a sliding tab for wind calculations. With practice, it can be manipulated with one hand, certainly a consideration when piloting an aircraft faced with an unplanned change of route.
The E6-B has been around a long time. Philip Dalton invented it in the early 1930s. During WWII, it was engraved brass, later plastic. Today, one can purchase aluminum, plastic, or cardboard models. Buy one if you are into realism and nostalgia. Try eBay and other auctions for better quality units at decent prices.
For ease, simplicity, accuracy, and speed, the flight-simmer should try the virtual E6-B. It is a freeware software program that calculates the Wind Correction Angle, Ground Speed, and a host of other things. See the illustrations below for the calculations just performed using the wind triangle.
Click here to download this handy utility.
With the basics of plotting and flying VFR courses behind us, the next step is instrument work. We'll begin with the Non Directional Beacon, NDB, because once you have mastered that work, you can handle all of the other IFR work with ease.
By now you will have noticed that all of the flight calculations involve "True Air Speed," TAS. Air Speed Indicators routinely display "Indicated Air Speed," IAS. The ASIs on Flight Simulator default into the IAS mode. ASIs become inaccurate as an aircraft climbs primarily because the air becomes thinner. So if your ASI displays 110 kts at 7500 ft altitude, your True Air Speed is actually higher.
Here is the rule of thumb to convert Indicated Air Speed to True Air Speed
Add two percent to the IAS for every 1000 ft above sea level.
Assume that your IAS is 110 kts, and you are flying at 4500 ft.
For short flights, the difference between IAS and TAS will not significantly impact your ground speed or Estimated Time En Route, ETE. For longer flights, it has a dual impact:
Compare the differences below when using IAS vs TAS for the calculations in the example flight from Lawrence, Mass. to Worcester, Mass.
The flight conditions for these calculations are:
|Flight Calculation||Using 110 kts IAS||Using 120 kts TAS|
|Ground Speed||90 kts||100 kts|
|Wind Correction Angle||20°||18°|
If your destination airport is 120 NM distant, using the 110 kts IAS for calculations instead of the correct 120 kts, you will arrive eight minutes earlier than planned. More significantly, you will be two degrees off course, which is about 4 NM. That's not real serious in good visibility when landing at an easy-to-find major International Airport. Missing a small grass airstrip by four miles in reduced visibility means you may not find it at all. More than a little embarrassing if it's an FAA examiner sitting next to you.
Some versions of Flight Simulator before FS2004 expressed winds aloft as True direction. If that is your sutuation, simply change the True winds to Mag winds for the wind triangle calculations. Do that by adding or subtracting the Magnetic Variation to the True directions.
As noted, winds in Microsoft's newer Flight Simulators are based on Magnetic north. In the real world of aviation, life is a bit more complicated. Surface winds are reported based on Magnetic north and winds aloft are reported based on True north. Thus WCA's are calculated using True Course and the winds aloft reports.
In early Flight Simulators, MS also showed winds based on True noirth. But since we flight sim pilots basically obtain magnectic course info when flight planning, magnetic north for winds aloft eased our calculations by eliminating one conversion factor.
NDB navigation is the next topic. It was a major breakthrough for airlines and enabled them to meet schedules almost without regard to weather. But there were aids to navigation before the proliferation of NDBs. Read how it all began in the next section. Learn about the early progression of navigation aids. I think you'll find it fascinating and you'll marvel at how well the early pilots did with these systems. Pioneering will have a new meaning.
Click on How it Began below to move on.
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© 1999 2008, Charles Wood.
Site best viewed at 600 × 800 resolution or higher.
© 1999 2008, Charles Wood.