General Explanations

Take Off and Arrival Information

Departure Field, Arrival Field
(input)

These are the identification codes for the fields. For example, the Waterloo-Wellington airport in Breslau has the code YKF and Pearson Airport in Toronto is YYZ.

Field Elevation
(input)

The elevation of the field above Mean Sea Level. For example, the Waterloo-Wellington airport is 1040 feet above Mean Sea Level.

Field Altimiter
(input)

The altimeter setting (barometric pressure) in inches of mercury at the field. This is obtained from the ground-level weather report for the field. Other information provided for the field at ground level by these weather reports includes: field temperature, wind velocity, wind track, dewpoint, visibility, ceiling, barometric pressure in kilopascals.

Field Pressure Altitude
(computed)

The standard altimeter setting is 29.92 inches of mercury. The difference between this and the actual altimeter setting, times the conversion of inches mercury into elevation, represents an altitude adjustment that is applied to the field elevation. This is covered in the books and is a simple formula of the form (A-B)*C+D. This provides an altitude correction resulting in standardized pressure.

Field Temperature
(input)

The temperature in degrees Celsius at the field, obtained from the ground-level weather report.

Field Difference Temperature
(computed)

The standard temperature under standardized pressure at Mean Sea Level is 15 degrees Celsius, and the temperature drops an average number of degrees for every thousand feet of corresponding standardized pressure decrease from Mean Sea Level up to a very high altitude. The average temperature decrease is known as the "lapse rate". According to the lapse rate decrease, the temperature at the field's pressure altitude should be one temperature, but the weather information says it is another. The Field Difference Temperature is simply the difference between what the standard temperature should be and what it really is.

Field Density Altitude
(computed)

This is the Field Pressure Altitude adjusted for the Field Difference Temperature. I was unable to find a published correction factor and I used linear regression on the charts and tables given in the books. I came up with the formula FPA+(111*FDT), which can probably be improved but gets within 80-90 percent of what the books report.

En Route Altitude
(input)

This is the altitude, in feet above Mean Sea Level, at which I hope to fly from Take Off to Arrival.

En Route RPM
(input)

This is the power setting, in Revolutions Per Minute, at which I expect to cruise.

En Route Temperature
(input)

This is obtained (or interpolated) from the upper winds weather information. Upper winds information provides temperature in degrees Celsius at 6000, 9000, 12000, and 18000 feet above Mean Sea Level, as well as Wind Track and Wind Velocity at these altitudes and 3000 feet.

En Route PA, DA, Diff. Temp
(computed)

The spreadsheet has two rows of Pressure Altitude, Temperature Difference, and Density Altitude figures for the en route cruise. These are calculated for the en route altitude from the Take Off upper winds and the Arrival upper winds, respectively. The calculations follow the same explanations as given for the fields. There is a third row, "En Route Average", that is simply the average of the Take Off and Arrival pressure and temperature figures. The rest of the spreadsheet uses these averages as the cruise conditions throughout the entire flight. Your program should be doing better than this by using such a linear average of this information between any two locations for which the ground and upper winds weather information has been entered.

Climb Performance Calculations

Pressure Altitude
(computed)

At this point in the spreadsheet we have Pressure Altitudes available for the Take Off field and for the En Route altitude (which will be reached within a few miles of the Take Off field). The field's ground and upper winds information should be used for both pressure altitudes. The Cessna 172 book has climb entries for pressure altitudes from Mean Sea Level up to a maximum altitude, and the first column on the left shows an interpolation between the two entries that bracket the Take Off field PA and the En Route PA. The interpolation factors are shown in the grey boxes.

Time, Fuel, Distance
(computed)

The figures from the climb table in the Cessna 172 book are shown bracketing figures for the field and the en route pressure altitude, as interpolated using the interpolation factors and then correcting for the difference temperature from the standard temperature at each of these pressure altitudes. The Cessna 172 book suggests a percentage correction of 10 per cent for each 10 degrees above standard temperature, and I have pro-rated that in the spreadsheet calculations.

Knots Indicated Airspeed
(computed)

This KIAS heading refers to the fifth column from the left. The figures from the climb table in the Cessna 172 book are shown bracketing interpolations computed by the spreadsheet.

KIAS, KCAS, KTAS
(computed)

This is the little table at the right of the climb performance calculation. KIAS stands for Knots Indicated Airspeed; KCAS stands for Knots Calibrated Airspeed, and KTAS stands for Knots True Airspeed. The device that measures airspeed is influenced by density altitude, and it does not measure linearly across all airspeeds. What you see in the plane on the guage is KIAS. The correction for the nonlinearity of the device gives KCAS. The KCAS reading, corrected for presurre altitude, gives KTAS. Two KIAS figures from the Cessna 172 book are shown bracketing the climb KIAS (the average of the field KIAS and en route KIAS shown in the fifth column from the left). This provides an interpolation factor shown in the grey box. The KCAS book entries corresponding to the two KIAS book entries are shown bracketing the interpolated KCAS figure produced using that factor. The KTAS is a correction added to KCAS, which I have taken as 0.00143 times the average of the Take Off and En Route density altitudes. This correction factor of 0.00143 for KCAS to KTAS is one I have had to determine from regression on the correction charts given in the book.

Cruise Performance Calculations

Initial Interpolation
(computed)

What is visible in the image just above are sections of the cruise performance tables (listed as the low and high rows) from the Cessna 172 book that bracket the En Route Pressure Altitude. There is one set of entries for each of the standard temperature at the given altitudes, 20 degrees Celsius below standard, and 20 degrees above. The PA entries provide an interpolation factor (in the grey box), and the mid rows represent the straight interpolation of PA and the quantities BHP (Brake Horse Power), KTAS, and GPH (Gallons Per Hour). The RPM figure is just repeated for reference and is not interpolated.

Subsequent Interpolation
(computed)

The interpolated BHP, KTAS, and GPH values, and the PA value, shown above provide three data points for a further interpolation. This image shows the results of a quadratic interpolation of those three data points and the subsequent evaluation of the parabola at the En Route temperature. The figures in grey show the divided difference table that was used for the quadratic interpolation, and the BHP, KTAS, and GPH values come from the parabola as evaluated at the actual En Route temperature.

KCAS, KIAS
(computed)

The KTAS value just produced, together with the Cessna 172 tables and the KCAS/KTAS correction formula are used to provide a KIAS value for the En Route conditions. During flight, the pilot will use the RPM setting, the altitude setting, and the KIAS setting to verify that he or she is tracking the conditions that the flight calculations are covering.

The Flight Plan

Overview

Each column represents a stage in the flight. It is the goal of every column to provide, at least, a total Time, a total Fuel consumption and a Magnetic Heading. All other information provides the input for calculations or some instrument reading that can be used as a reference.

TO->Alt. is the climb to the En Route altitude. Alt.->SHP is the subsequent short stage at that altitude to reach the Set Heading Point. Each subsequent column is a Way Point transit (SHP->First, First->Second, etc.). Not shown is a column that registers the Descent Point (which the spreadsheet does not calculate) and a column that tries to account for the details of entering the pattern, landing, and taxiing at the Arrival (Destination) Field.

The Alt->SHP, SHP->WP, WP->WP, and WP->DP legs all use the cruise information (appropriately interpolated along the way from weather information that must be provided at Take Off and Arrival fields and may be provided at some of the Way Points in between).

Descent

The leg from Descent Point (DP) to Landing Pattern Entry is flown at the same KIAS as the Way Point Legs, but at a reduced power setting. This reduced setting is directly related to the rate of descent that is input. (x RPM reduction results in y Feet Per Minute of descent at the constantly held KIAS, for a Cessna 172 x=1000 results in y=100). The ground speed and time are usually taken as the equivalent of the cruise conditions, but the fuel consumption will be reduced.

Take Off and Landing

The time and fuel consumption of both of these legs are a combination of estimates and calculations. An estimate for landing is that it is the equivalent of something like six minutes of descent flight, but your program might like to ask for an estimate in terms of minutes instead of assuming six. For take off, the Cessna 172 book provides an estimate ("taxi and run up"), and for climb, the book provides calculation assistance ("climb performance table").

The Rows of the Flight Plan

MOCA

Ignore this one. It is the Minimum Obstruction Clearance Altitude, and the pilot would use that for his/her own reference to check that the Altitude was sufficient.

Altitude

The cruise altitude, which was input for the first part of the spreadsheet and which you may assume constant from Alt to DP.

KIAS, KTAS

The KIAS/KTAS information from the first part of the spreadsheet.

True Track
(input)

The angle, from true north, as measured on an aviation map, that must be taken as a direction to get from one location to the next.

Distance from Last
(input)

The distance, as measured on an aviation map, that must be taken to get from one location to the next. (On the climb, the first part of the spreadsheet calculates what distance the plane covers to reach altitude, so this is not input. Instead, the TO->SHP distance is input; the TO->Alt distance is computed, and the Alt->SHP distance is the difference. Similar considerations apply to the last WP, the DP, and the Arrival Field.)

Wind Track and Wind Velocity
(input/interpolated)

WT and WV are provided by the weather reports on ground and for upper winds. This will be provided at the Take Off and at the Arrival Fields and may be provided at any WP inbetween. For other way points, use the linear (pro-rated) average. between the previous and the next information along the path. That is; if WP1 and WPK have this information and WPJ is 20 percent of the way in flight distance from WP1 and WPK, then assign the Wind Track value of 0.80*WT1 + 0.20*WTK to Wind Track J.

Correction Angle
(computed)

The Wind Track (WT) and the True Track (TT) and the Wind Velocity (WV) and my Velocity (KTAS) set up a small vector problem that produces the vector I should be taking instead of the TT/KTAS vector I am taking. In polar representation the solution to this problem can given as an angle I should turn away from my TT in order to be flying a track that will actually take me to the point I wish to reach. (For the climb column, the spreadsheed fakes KTAS by figuring out the Ground Speed as distance divided by time and backtracks that GS into an equivalent KTAS.)

True Heading
(computed)

The True Heading (TH) is the True Track adjusted by the Correction Angle.

Magnetic Heading
(computed)

Unfortunately, the pilot has no way of referencing true north in order to fly by True Heading. So the pilot flies according to Magnetic Heading (MH) instead. The difference between true north and magnetic north is the Magnetic Variation, and this variation at the WP must be added to the True Heading to produce the Magnetic Heading.

Magnetic Variation
(input)

This will be provided for every WP.

Ground Speed
(computed)

The plane is flying at KTAS in the True Heading direction, but the plane is actually progressing along the True Track. So there is an obvious trigonometric adjustment to the KTAS to produce the Ground Speed, the actual speed along the True Track.

Air Time
(computed)

This is simply the time required to go the distance. The Ground Speed and the Distance from Last give this directly. (In the climb column, the climb calculations provide the time instead.)

Added Flight Time
(input)

This is a little funny. Flight time is the time the motor is running. Air time is the flight time that is spent with the wheels off the ground. The Added Flight Time is an estimate for such things as taxi and run up. The Cessna 172 book provides Take Off taxi and run up estimates. For taxi at landing a rule-of-thumb estimate is something like six minutes, but your program might like to ask for an estimate.

Taxi Fuel
(input)

This is actually taxi and run up fuel on take off and just taxi fuel for landing. By way of explanation: in order to take off, the pilot taxis to the end of the runway. At the end of the runway, before asking for take-off clearance, the pilot then goes through a checklist that puts the engine through its paces to try to detect any problems. This involves running the motor up to a higher speed and then down to idle, among other things, and it burns enough fuel that it should be included in the calculations. The handbook for an airplane will usually provide an average estimate for taxi and run up. The pilot will usually estimate taxi fuel upon landing from his/her own experience.

Climb/Descent Fuel
(computed)

The climb fuel is computed in the first part of the spreadsheet. The descent fuel is reasonably estimated as the fuel rate at the reduced power setting of descent multiplied by the sum of the descent and landing times.

En Route Fuel Rate
(computed)

This is the cruise fuel consumption rate (GPH) from the performance calculations in the first part of the spreadsheet.

En Route Fuel
(computed)

This is the cruise fuel consumption rate times the Air Time for each WP->WP leg (or Alt->SHP or WP->DP leg).

Total Fuel
(computed)

The sum of all the fuel used in the column.

Reserve
(computed)

The law requires that the flight be undertaken with enough fuel to reach the destination and then continue for 45 minutes further. This 45 minutes of reserve is a safety factor that provides a way of trying to reach an alternative field in an emergency, as well as to provide a buffer for the trip even if no emergency arises. This reserve is calculated as 3/4 times the En Route GPH value.

Total
(computed)

The grand fuel total of the reserve and all the column totals.