Multi-Engine Math

The following article appeared in the July 2018 issue of the American Bonanza Society Magazine - www.bonanza.org

It was because of the oral exam for my ATP check ride a number of years ago that caused me to think more about risk management in flying multi-engine aircraft and to dig deeper into the preflight effort I was putting into some of these flights - One of them stoked by the following scenario:

For a given airport, on a given day (take today and your home airport for example) if you departed IFR with ceiling at 300 overcast, and lost an engine just as you entered the overcast, what would you do?  Let's say you were able to quickly identify, verify and feather. 

The most basic answer, and the one I gave, would be to declare an emergency and ask for vectors to the ILS back to the airport.  We had a good discussion about risk management and aeronautical decision making, but my attempt at trying to avoid doing math on this check ride was futile.

The examiner wanted to know many miles would it take me to reach MSA (Minimum Sector Altitude), whether we can comply with Obstacle Departure Procedure (ODP) for this airport and whether this was going to be a problem with one engine inoperative.

I started looking at the approach procedures for the airport to look for obstructions, checked the obstacle departure procedures and even looked at the sectional.  It looked like I was not going to be able to make the minimum climb gradient as described by the ODP (260 feet per mile) and decided that a course about 10 degrees right of the runway centerline would keep me relatively clear of any big sticks poking out of the earth.  With that figured out, I calculated my single-engine climb rate and it was going to be a dismal 240 feet per minute.  If I'm traveling about 90 knots over the ground and need to climb 1200 ft to be at MSA, that's going to take 5 agonizing minutes.  Going 1.5 miles per minute, that puts me 7 ½ miles out!

Math Class

To break down the math, I always like to first understand how many miles I cover in a minute.  This is one of those equations you recall from your private pilot days:

                                MPM=GS/60

Plugging in our ground speed of 90 knots on departure:

                                MPM=90/60

You do remember that we have to use Ground speeds, right? I came up with 90 since we had a nice headwind and it makes for easy math for this example.

                                MPM = 1.5

Single engine climb rate is determined by interpreting the charts located in the performance section of your Pilots Operating Handbook.  For a given weight and atmospheric conditions, you will arrive at a generous figure that you are lucky to obtain. Let's say for our example, this figure is 240 ft per minute. 

Find MSA for the airport by using one of the approach charts for the departure airport and find out how many feet you need to climb in order to get to that altitude if you lost an engine at 200ft.

If we need to climb 1200 feet to get to the MSA, which doesn't seem too difficult, the math looks like this:

                1200/240 = 5 minutes

Now how many miles is this going to take? 

                5 Minutes X 1.5 (Our miles per minute calculation from above) = 7.5

If you do everything perfectly, you will be able to climb 1200 feet in 7.5 miles.  Add some time for level off, building some speed and feeling comfortable with complying with ATC instructions, you are easily over 10 miles out. 

One might ask, do we really need to climb up to MSA?  The answer is no, but it was a good enough setup for getting me to pull out the calculator to do some math.   Another scenario has us looking at the ODP.  When trying to determine whether you are going to be able to meet the minimum climb gradient dictated by the ODP, you will remember from your instrument training days, that this is in feet per nautical mile.

We know that we can climb at 240ft per minute, but how does that translate to feet per nautical mile? If we take our formula to determine how many miles we cover in a minute (MPM=GS/60), we came up with 1.5.  We can take this number and multiply it by our required climb gradient from the ODP (260 feet per minute) and come up with a required climb rate of 360 feet per minute – Not good enough since our single-engine climb rate is 240 feet per minute.

A note about ODP

In the age of electronic charts, finding Obstacle Departure Procedures isn’t as simple as looking in the front of the Terminal Procedures Publication.  You should become familiar with how to get this information in your favorite electronic flight bag – it’s not always obvious in some of the tablet apps out there.  I use Fltplan Go, and ODPs are located under procedures, by selecting take off minimums.  In ForeFlight, you need to go to the Procedures sub-tab of the airport and select Departure.

Summary

This exercise is intended to get you thinking of what would happen when an engine fails at the most inopportune time and understand where you are going to point the nose once you get things under control.  There may be cases when you might want to wait for better weather, so you can be on the lookout for obstacles or reduce the weight so you can achieve minimum climb gradient.

 

This also goes for VFR weather too.  IFR demands are high, and there are procedures we need to follow to get back to the airport, but we need to exercise caution when VFR too.  A low altitude engine failure in VFR weather shouldn’t mean that the pilot’s default response is to make a quick left downwind turn to get back to the airport all the while trying to gain some altitude.  

A straight-ahead plan that has no obstacles might be a better idea.  Besides, is a turn at low altitude with an engine failure really a good idea?  At my airport - Gary, Indiana - we have four large antennas at 500ft AGL just south of the airport on downwind for Runway 30.  This could be disastrous if I was anxious to turn on downwind too quickly.
For the most part, all of this math is not even necessary as there are many apps out there to choose from, as well as tables (e.g. Climb/Descent Table) in the Terminal Procedures Publication and Pilots Operating Handbooks to help you arrive at the same conclusion, but sometimes I feel that doing the calculations help solidify concepts and keep you fresh. 

Whether they are deliberately thought out or not, we all make risk-based decisions before every flight that include the capabilities of our aircraft, our personal capabilities and the environment we fly in. Flying multi-engine aircraft, we need to dig deep into the risk associated with engine failure and have a plan of action if and when it happens at the most inopportune time. Running through scenario-based exercises such as this helps fine-tune our thought process and keep us sharp.