What is the maximum amount of fuel that may be aboard the airplane on takeoff if loaded as follows?
For the first question, we are given the empty weight of the airplane, pilot and front passenger weight as well as the weights for the rear passengers and baggage. The chart tells us that the oil weighs 15 pounds.
To start, we need to add all the weights together as shown in figure 2 below.
After adding the weights together, we can see that the weight of the airplane is 2,060 pounds.
Next, we can see from the weight table that the max allowable weight is 2,300 as illustrated by the arrow in figure 3 below.
We then need to subtract the weight of the airplane from the max weight allowable to find how much weight capacity is left for extra fuel. The max weight of 2,300 pounds less the airplane weight of 2,060 pounds equals 240 pounds as shown in figure 4 below.
Fuel weighs 6 pounds per gallon so we would then divide 240 by 6 to find the max fuel amount of 40 gallons. The correct answer for question 1 is “A.”
If an airplane weighs 2,300 pounds, what approximate weight would the airplane structure be required to support during a 60-degree banked turn while maintaining altitude?
The answer to this problem is fairly straight forward, just find the angle of bank (which in this case is 60 degrees) and multiply the airplane weight by the load factor. The load factor at a 60-degree angle of bank is 2. Multiply the airplane weight by two to find the correct answer of 4,600 pounds.
Calculate the moment of the airplane and determine which category is applicable.
During your private pilot written knowledge test, you will be given a booklet with weight and balance tables similar to the ones shown in figure 8.
To solve this problem, we would use a straight edge and draw lines from the corresponding weights on the left of the chart (see figure 9 below). We would draw the line over to intersect the line that corresponds to the weight we are trying to solve for.
To find the weight for the pilot and front seat passenger draw a line just above the 300 number on the left since the weight is 310 pounds for the front passenger and pilot. Draw the line from the left to right until the line intersects the pilot and front passenger line in the chart. We then draw a line down to the bottom of the chart to find the aircrafts moment divided by 1,000. We can see the moment divided by 1,000 is about 11.7 for the pilot and front passenger.
Repeat the same process for all the other weights. The moment divided by 1,000 for the rear passengers is 7 and the moment for the fuel is 11.2 to be exact. It can sometimes be difficult to find the exact figures on the weight and balance tables so try to get as close as possible but sometimes you can round up or down slightly and will still get very close to the right answer.
We then add all the moment figures together and the weights to find the center of gravity (CG) and weight of the aircraft. See figure 10 in the chart below.
We then draw two lines in the chart in figure 11. One from the left just under the number 2,000 (since the airplane’s weight is 1,999 pounds). Then draw a 2nd line up from the bottom of the chart just to the right of the number 80 since the airplane’s moment divided by 1,000 is 81.2. The lines intersect at the upper right-hand range of the utility category. Therefore, the correct answer is “C.” The airplane’s moment divided by 1,000 is 81.2 and the aircraft is in the utility category.
What effect does a 35-gallon fuel burn (main tanks) have on the weight and balance if the airplane weighed 2,890 pounds and the moment divided by 100 was 2,452 at takeoff?
We know that 35 gallons of fuel weighs 210 pounds since one gallon of fuel weighs 6 pounds. You can see from the fuel weight table (figure 14 below) that the moment for 35 gallons of fuel is 158.
To summarize, the aircrafts moment at takeoff was 2,452. We can subtract the fuel’s moment of 158 to get the aircrafts moment after 35 gallons of fuel burn. The aircrafts moment after the 35 gallons of fuel burn is now 2,294. The aircrafts weight is reduced from 2,890 pounds to 2,680 pounds. Notice from the figure to the bottom right of the chart the aircraft’s moment limits for a given weight. Since the aircraft is now 2,680 pounds, we can see the 35-gallon fuel burn would reduce the aircraft’s weight by 210 pounds and the center of gravity (CG) is now aft of limits. Therefore, the correct answer to question 4 is A. The airplane’s weight is reduced by 210 pounds and the CG is aft of limits since 2,294 is greater than the aft limit of 2,287.
If 50 pounds of weight is located at point X and 100 pounds at point Z, how much weight must be located at point Y to balance the plank?
To solve this problem, we need to find the moment for points “X” and “Z” on the plank.
The formula to find the moment is weight multiplied by arm. We can find the moment for point “Z” by multiplying the weight of 100 pounds by the arm of 100 inches. The moment for point Z is 10,000. We will use the same formula to find the moment for point X. 50 times 50 equals 2,500.
We then subtract point X’s moment of 2,500 from point Z’s moment of 10,000 to get 7,500. We would then divide 7,500 by 25 since that is the length of point “Y” from the center of gravity. 7,500 divided by 25 equals 300. Thus, we would need to place 300 pounds at point “Y” to balance the plank.
