This is the example to calculate takeoff distance from graph as given on page 8-30 of the “Private Pilot Test Prep 2015”. In the example we are given the following parameters:
Outside air temperature: 90 F
Pressure altitude: 2000 ft
Takeoff weight: 2500 lbs
Headwind component of wind: 20 knots
Step 1: Use the temperature provided and draw a vertical line to intercept the appropriate pressure altitude curves.
Step 2: Go horizontally till you reach reference line #1. This is your density altitude. This is how high (or low) the plane “feels” it is sitting when non-standard pressure and temperature are accounted for.
Step 3: From the point on the first reference line go down, diagonally, staying proportionally distant from the two lines between which you are plotting, till you intercept your weight line. Staying proportionally distant between the two lines means if you start half way, stay half way till you intercept the weight line, or a third of the way between the line or whatever the case maybe. But try to stay equi-distant from the two lines as far as possible.
Step 4: From this point again go right horizontally till you intercept reference line #2. This point is your takeoff roll if wind conditions are “calm”.
Step 5: If you do have a headwind component, then proceed plotting to the right diagonally down. Again as in step 3, stay proportionally distant from the two lines between which you are plotting your line, to intercept the headwind component.
Step 6: Plot a horizontal line to the right. Where this intercepts reference line #3, draw two lines. One horizontal to get the takeoff roll (Step 6a). The other diagonally up, following the closest curve to represent the total distance to the 50 foot obstacle from the start of the takeoff (Step 6b).
Following these plots (solid red line) you will get a takeoff roll of approximately 500 feet and a total distance to the 50ft obstacle of approximately 1000 feet. These distances are OK to answer the FAA Knowledge test. But for practical purposes, to add a margin of safety, we can add an additional 50% to get a takeoff roll of 600 feet.
Also from the weight and takeoff speed inset, it is seen that for 2500 lbs you can extrapolate and see that the approximate speed at takeoff is 62 knots at end of roll and 67 knots at 50 feet, which is also Vx.