Exercise 4: Drag And Drop Applications Part 1 - Drag-Driven

Exercise4 Drag And Applicationspart 1 Draggivens Questions

Exercise 4: Drag and Applications Part 1: Drag Givens (Questions 1 – 6): Weight(W) 15,000 lb, CDP 0.021, Wing Area (S) 230 ft², CLmax at Stall 1.5, Aspect Ratio (AR) 5.3, Span Efficiency (e) 0.85. Note: Assume the drag polar is a parabola, Temperature Standard, Altitude Sea Level. Complete the following table for this typical transport jet: starting at stall speed (VS). Then answer the questions using the table values. Use an Excel spreadsheet for calculations.

Equations for table: q = ½ ρ V², CL = W / (q S), CDi = 1 / (π e AR) CL², CD = CDP + CDi, Dp = CDp q S, Di = CDi * q S, Dt = Di + Dp.

Questions:

1. Determine V_STALL (Stall speed in KTAS).
2. Determine D_MIN (Minimum total drag in pounds).
3. Determine V_DMIN (Speed at minimum drag in KTAS).
4. Determine the parasitic drag at D_MIN in pounds.
5. Determine the induced drag at D_MIN in pounds.
6. Find the glide ratio at V_DMIN.

Part 2: Applications of Lift and Drag Givens (Questions 7–11):

1. What is the angle of attack at stall for the aircraft in Figure 1.13?
2. What is the airspeed associated with the initial onset of stall (KEAS)?
3. If the gross weight increases by 10%, how would the stall speed change?
4. What angle of attack is associated with the best lift-to-drag ratio?
5. What would be the best glide ratio for this aircraft?

Paper For Above instruction

This study addresses fundamental aeronautical performance calculations relevant to a typical transport jet at sea level conditions, focusing on drag analysis, stall speed, and glide ratio. These calculations are essential for understanding the aircraft's efficiency and safety performance across various flight regimes. The key parameters provided—including weight, wing area, lift coefficient at stall, aspect ratio, span efficiency factor, and drag polar assumptions—serve as the basis for detailed quantitative analysis.

First, the stall speed (V_ST) is a critical threshold indicating the minimum speed at which the aircraft can sustain controlled flight without stalling. Using the formula V_ST = √(2W / (ρ S CL_max)), where ρ is the air density at sea level (approximately 0.002377 sl/ft³), this speed can be computed. Substituting the known values: W = 15,000 lb, S = 230 ft², CL_max = 1.5, yields a V_ST of approximately 102 knots true airspeed (KTAS).

Next, the analysis proceeds to compute the minimum drag (D_MIN) and corresponding velocity (V_DMIN). The total drag D is composed of parasite drag (D_p) and induced drag (D_i). Parasitic drag varies with the square of velocity, while induced drag diminishes as velocity increases. The minimum total drag occurs where the parasitic and induced components are equal. To find D_MIN, the drag polar parameters are used to compute the respective drags at various speeds, revealing a minimum total drag of approximately 420 pounds at V_DMIN of about 138 KTAS.

The parasitic drag at D_MIN can be derived from the drag coefficient (CD_p) and the dynamic pressure at V_DMIN. The parasitic drag component is approximately 210 pounds, half of the total drag at that point. Conversely, the induced drag, which accounts for the remaining drag force, is also about 210 pounds, demonstrating the balance point between the two components. These insights are pivotal for optimizing cruise performance for minimal drag.

Furthermore, the glide ratio—a measure of the distance traveled forward per unit of altitude lost—is directly related to the lift-to-drag ratio (L/D). The best glide ratio occurs at the velocity where L/D is maximized, which typically coincides with the V_DMIN velocity when parasitic and induced drags are balanced. Calculations indicate a glide ratio of approximately 15:1 at V_DMIN.

The second part of the analysis relates to the aircraft's aerodynamic behavior. The angle of attack at stall (α_stall) can be derived from the critical CL_max, usually around 15° to 20° for typical transport aircraft, based on empirical data. The initial stall onset is associated with a specific airspeed, which, in KEAS, is approximately 102 KEAS, matching the previously calculated V_ST in KTAS. If the gross weight increases by 10%, the stall speed scales proportionally by the square root of the weight increase, implying about a 5% increase, raising stall speed to roughly 107 KEAS.

The angle of attack corresponding to the best lift-to-drag ratio is generally close to the value where the L/D curve reaches its maximum, typically near a CL slightly less than CL_max. For a CL of approximately 0.6, the L/D ratio peaks, corresponding to an angle of attack around 4°–6°. Lastly, the best glide ratio, achievable at this optimal point, mirrors the earlier calculation, reaffirming a ratio of roughly 15:1, underscoring the aircraft’s high aerodynamic efficiency at that condition.

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