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So why is this important to understand? Once the ROT is understood, a pilot can determine the distance required to make that particular turn which is explained in radius of turn.
Radius of Turn
The radius of turn is directly linked to the ROT, which explained earlier is a function of both bank angle and airspeed. If the bank angle is held constant and the airspeed is increased, the radius of the turn changes (increases). A higher airspeed causes the aircraft to travel through a longer arc due to a greater speed. An aircraft traveling at 120 knots is able to turn a 360° circle in a tighter radius than an aircraft traveling at 240 knots. In order to compensate for the increase in airspeed, the bank angle would need to be increased.
The radius of turn (R) can be computed using a simple formula. The radius of turn is equal to the velocity squared (V2) divided by 11.26 times the tangent of the bank angle.
R = V2
11.26 x tangent of bank angle
Using the examples provided in Figures 4-48 through 4-50, the turn radius for each of the two speeds can be computed. Note that if the speed is doubled, the radius is squared. [Figures 4-51 and 4-52]
4-35
240 knots
11.26 x tangent of bank angleR = 240211.26 x tangent of 30°R =V2R =11.26 x 0.57735 57,600R = 8,861 feet (four times the radius at 120 knots)The radius of a turn required by an aircraft traveling at 240 knots using the same bank angle in Figure 4-51 is 8,861 feet. Speed is a major factor in a turn.
Figure 4-52. Radius at 240 knots.
Figure 4-53. Another formula that can be used for radius.
r = speed (fps) x
360ROTPi (π)2202.8 x 68.6π2r =13,912π2r =4,4282r == 2,214 feet
Another way to determine the radius of turn is speed in using feet per second (fps), π (3.1415) and the ROT. Using the example on page 4-34 in the upper right column, it was determined that an aircraft with a ROT of 5.25 degrees per second required 68.6 seconds to make a complete circle. An aircraft’s speed (in knots) can be converted to fps by multiplying it by a constant of 1.69. Therefore, an aircraft traveling at 120 knots (TAS) travels at 202.8 fps. Knowing the speed in fps (202.8) multiplied by the time an aircraft takes to complete a circle (68.6 seconds) can determine the size of the circle; 202.8 times 68.6 equals 13,912 feet. Dividing by π yields a diameter of 4,428 feet, which when divided by 2 equals a radius of 2,214 feet [Figure 4-53], a foot within that determined through use of the formula in Figure 4-51.
In Figure 4-54, the pilot enters a canyon and decides to turn 180° to exit. The pilot uses a 30° bank angle in his turn.
Weight and Balance
The aircraft’s weight and balance data is important information for a pilot that must be frequently reevaluated. Although the aircraft was weighed during the certification process, this data is not valid indefinitely. Equipment changes or modifications affect the weight and balance data. Too often pilots reduce the aircraft weight and balance into a “rule of thumb” such as: “If I have three passengers, I can load only 100 gallons of fuel; four passengers, 70 gallons.”
Weight and balance computations should be part of every preflight briefing. Never assume three passengers are always of equal weight. Instead, do a full computation of all items to be loaded on the aircraft, including baggage, as well as the pilot and passenger. It is recommended that all bags be weighed to make a precise computation of how the aircraft CG is positioned.
The importance of the CG was stressed in the discussion of stability, controllability, and performance. Unequal load distribution causes accidents. A competent pilot understands and respects the effects of CG on an aircraft.
Weight and balance are critical components in the utilization of an aircraft to its fullest potential. The pilot must know how much fuel can be loaded onto the aircraft without violating CG limits, as well as weight limits to conduct long or short flights with or without a full complement of allowable passengers. For example, an aircraft has four seats and can carry 60 gallons of fuel. How many passengers can the aircraft safely carry? Can all those seats be occupied at all times with the varying fuel loads? Four people who each weigh 150 pounds leads to a different weight and balance computation than four people who each weigh 200 pounds. The second scenario loads an additional 200 pounds onto the aircraft and is equal to about 30 gallons of fuel.
The additional weight may or may not place the CG outside of the CG envelope, but the maximum gross weight could be exceeded. The excess weight can overstress the aircraft and degrade the performance.
Aircraft are certificated for weight and balance for two principal reasons:
1. The effect of the weight on the aircraft’s primary structure and its performance characteristics
2. The effect of the location of this weight on flight characteristics, particularly in stall and spin recovery and stability
　
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