VFR Formula Cheat Sheet

Download Pilot fomula cheat sheet

Above is a quick reference cheat sheet with formulas needed for the VFR pilot.
Below is an amplified guide and explanation for each formula.

VA

What is Va, and why does it change?

Va is the maximum speed at which we would stall before we damaged the airframe, if a sudden full-scale deflection were made of the controls.

Lets imagine we’re flying straight and level. We grab the yoke and pull full back pressure (nose up). We would feel a lot of G’s (load factor)! If we pull up too suddenly or to much, we would exceed the load factor limitations of our airplane (a very real limitation, found in the POH). Exceeding this limit will damage our airplanes body, “airframe”. We want to avoid breaking our plane, of course! So, what choice do we have instead of breaking our plane?

Lets imagine we’re back again flying straight and level like before. This time, before we grab the yoke and pull up, lets slow down below. Now that we’re slower, we are closer to our critical angle of attack. So, when we begin pulling up, we will exceed our critical angle of attack (and stall) sooner than before! By stalling sooner, our nose will drop, and reduce our load factor immediately, and thus avoid structural damage.

Aircraft manufacturers publish Va at MAX takeoff weight, but very often, we aren’t flying at max takeoff weight. So, we should calculate Va before our flight, especially if we’re planning on doing maneuvers.

NOTE: although the above example discusses straight and “pulling G’s”, but remember that structural damage can occur any time load factor limitations are exceeded (including turns and maneuver).

HOW TO CALCULATE:

1. Get your scientific calculator and type in todays current takeoff weight.
2. Divide it by your aircrafts MAX takeoff weight, to get a small number
3. square root the small number.
4. Multiply the rooted number by your aircrafts Va at max takeoff weight to find your answer.

Your answer is the maximums speed at which you will stall before you incur structural damage to your airplane. During maneuvering or extreme turbulence, it is important to fly below Va.

 

True Air Speed

True airspeed is our speed through the air, without the errors of position error, and temperature & pressure errors. It is the speed we are truely flying through the air at. For an exanded explaination of true airspeed, please reference: THIS ARTICLE.

We calculate with an E6B. This “Rule of thumb” is a good estimation tool to use, perhaps in flight, when a calculator is not accessible.

How to use it:
“Our TAS increases by 2% for every 1,000ft high we are MSL”.
1. Find 2% of our pressure altitude

2. multiply the result by our calibrated airspeed

This is only an APPROXIMATION. For precise application, an E6B is to be used.

Moment

Think of moment as the “total force” of an object. Whats the difference between pushing a door open from the knob, as opposed to pushing it from the hinge-edge?
Imagine pushing a door open with the same force you normally do, only this time, instead of pushing from the knob, you push from the opposite edge of the door. Does the door move faster or slower than usual? This is an example of leverage and moment.
Moment is a force (your hand) multiplied by a distance, “arm” (the distance from the hinge of the door). When you push the door a long distance or, arm, your hands force is multiplied. when you push the door from a small distance from its hinges, a “small arm”, the force is multiplied by only the tiny distance, and so the total force, “moment” is quite small, and doesn’t push the door as fast.

Moment = Force x arm

Why do we need to know this?
We will need to do weight and balance calculations. Knowing the total force of an object is very important when we’d like to balance our airplane in a specific point.

 

C.G.

What is Center of Gravity? How is it measured? Why does it matter?

Try balancing a pencil on your finger. When perfectly balanced, notice the point at which you’re resting the pencil on. This location is the center of gravity.

The center of gravity is the point where gravity acts on an object. As seen in our pencil example, this balancing point is a very real location. How do we measure the location of our C.G? We will be measuring distance. Our C.G. is a certain distance from the tip of our pencil. We could say, “The C.G. of our pencil is 6 inches from the tip”. We chose the tip of the pencil to measure against because it is convenient. We could, choose instead to measure the distance from the exposed wood of the pencil. Lets call this point we measure from, the “datum”. Datum simply means reference point. When we ask our friend the C.G. Location of their pencil, they will need to tell us the distance, and where the “datum” point is on their pencil (ie, x inches from the tip).

Why does C.G. Matter?

Our aircraft manufacturer has published limitations to our C.G. Location.
What happens if we exceed our C.G. Limitations, what will happen?
If our C.G. is too far forward, we call this “nose heavy-ness”. Results of nose heaviness are:

• Difficult rotation / flare on runway
• Longer takeoff distance
• Slower cruise speed (at given RPM)
• Increased stall speed
• Better stall recovery

If our C.G. is too far aft, we call this “tail heavy-ness”. Results of tail heaviness are:

• Easier rotation / flare on runway
• Shorter takeoff distance
• Faster cruise speed (at given RPM)
• Decreased stall speed
• Worse stall recovery

Why do each of these occur? – Read PHAK chapter 10.
The point is: our C.G. affects our handling charactaristics. Compare and contrast each difference of forward vs aft C.G. Is one better than the other?

The distance of our C.G. from our “reference point”, or Datum, is found by dividing our total moment by our total weight.

A future article will be linked with an expanded explanation of C.G. Numerous articles have already been written about the subject.

Weight Change

If our loading changes during pre-flight, we could either recalculate our weight-and-balance all over again, or we could use a simple formula to calculate the effect of the change.

Its basic Algebra.

1. Identify what you need, mark it as X
2. fill in the rest of the numbers
3. Solve for X
4. Apply X to your current weight and balance, to find the new weight and balance information.

Lets suppose we need to find our new C.G. after our passenger decides to sit in the back seat, instead of the front seat.
Before our passenger moves, the C.G. is: (41 inches)

Our weight to be changed is the weight of the passenger (170lbs)

Our Total weight is the takeoff weight of our airplane (2350lbs)

Our change in C.G. is what we are trying to find! (X)

Our distance changed would be the distance between the front seat and the back seat (since the passenger is moving from the front to the back seat). (40 inches)

From here, we can solve for X.
X = 2.89
This means, our Change in C.G. is 2.89. Notice, this number is positive (not negative), so, we ADD it to our C.G. location.
So, our NEW C.G. would be 43.89

Notice, this logically makes sense, we are moving more weight to the back, so our C.G. moves aft with the weight. If we were to move weight forward, we would expect to see the C.G. decrease and come forward as well.

Glide Distance

In our small training aircraft, a good rule of thumb can be used to estimate our glide distance. The saying goes, “for every thousand feet high, you can glide 1.5NM”
We can quickly in flight estimate our range in an engine-out scenario with this rule of thumb.
Our Height AGL divided by 1000 gives us our “thousands” of feet. Then multiplying by 1.5 gives us the miles we can glide.

 

Pressure Altitude

Our Pressure altitude can easily be found by setting our altimeter to 29.92 and reading the altitude indicated. If we are away from our aircraft, we can either use our pressure altitude chart, or this formula to find our pressure altitude.

 

Density Altitude

Density altitude can be computed with an E6B or using this formula. Density altitude is the altitude the airplane feels like its at. If we are taking of from a field elevation of 200MSL, but the density altitude comes out to be 3,000, This means our aircraft will perform as if it were at 3,000 MSL!

NOTE: You may ask: If density altitude is where our airplane feels like its at, why are our performance charts (in most airplanes) using pressure altitude not Density altitude?
When these aircraft performance charts were made, in the 1980’s, computers were in there infancy, and requiring a pilot to compute Density Altitude before every flight was very cumbersome. Instead the pilot can simply twist their altimeter to 29.92 and read pressure altitude, and take a glance at their thermometer and easily find their performance data. Today, we can still simply use PA and Temp to get our performance data. Density altitude is still important for us pilots to know, though, because it tells us exactly how high the airplane feels like its at, which can be a clear warning sign of poor performance.

 

Standard Temperature at Altitude

In our cruise performance charts, we need to determine if the temperature at our cruise altitude is above or below what is standard at that altitude. We need to compare the actual temperature aloft (from winds aloft chart) to the theoretical standard temperature. We can simply draw out the 15 degrees at sea level, and draw each thousand feet, and subtract by 2 in a nice drawing. That method does work. This formula is more simple and is faster.

 

Cloud Height

Why is our temperature and dew point spread important?
If our temperature cools to our dew-point, visible moisture will form! If this concept is not understood, further study of cloud and fog formation is needed, the PHAK is a good rescource for this.
As we climb, our temperature decreases, we call the rate at which the temperature decreases the “temperature lapse rate”. Our dewpoint also decreases as altitude increases.
Our Standard temperature lapse rate is 2 degrees C per 1,000ft.
Our dewpoint will aslo decrease at a rate of 0.5 degrees C per 1,000ft.
This formula finds the altitude will our temperature “catch up” to our dewpoint.
When our temperature and dewpoint are the same (our temperature “catches up”), then in theory, clouds could form. So this formula estimates the height AGL clouds could form.

NOTE: This formula is not a dead-set guarantee of clouds, other factors such as condensation nuclei make this formula only an estimation.