Wing Area and Engine Sizing
In this part of design phase, you are to obtain:
1. wing reference area (S or Sref );
2. engine thrust (T) for Jet driven or engine power (P) for
propeller driven.
Wing Area and Engine Sizing
The aircraft performance requirements utilized to size the aircraft
in this step are:
Wing Area and Engine Sizing
In this section, three new parameters appear in almost all
equations are needed to be defined first.
• Wing loading
• Thrust-to-weight ratio
• Power loading
Wing Area and Engine Sizing
In general, two desired parameters (S and T (or P)) are
determined in six steps. If jet-driven, substitute the words thrust
loading (T/W) instead of power loading (W/P).
1. Derive one equation for each aircraft performance
requirement (e.g., Vs, Vmax, ROC, STO, hc, Rturn, ωturn)
Wing Area and Engine Sizing
2. Sketch all derived equations in one plot. The vertical axis is
power loading (W /P) for propeller driven, or trust loading for
jet, and the horizontal axis is wing loading (W /S). Thus, the
plot illustrates the variations of power loading with respect to
wing loading.
Wing Area and Engine Sizing
3. Identify the acceptable region inside the regions that are
produced by the axes and the graphs. The acceptable region
is the region that meets all aircraft performance
requirements.
For Propeller Driven
For Jet Driven
Wing Area and Engine Sizing
4. Determine the design point. The design point on the plot is
only one point that yields the smallest engine in terms of
power. For the case of the jet aircraft, the design point yields
an engine with the smallest thrust.
Wing Area and Engine Sizing
5. From the design point, obtain two numbers:
corresponding wing loading (W /S)d and corresponding
power loading (W /P)d.
6. Calculate the wing area and engine power from these two
values, since the aircraft MTOW (WTO) has been
determined previously.
Stall Speed
xxx
Stall Speed
Based on FAR Part 23, a single-engine aircraft and also a multi-engine
aircraft with a MTOW of less than 6000 lb may not have a stall speed
greater than 61 knot. A very light aircraft (VLA) that is certified with
EASA3 may not have a stall speed greater than 45 knot:
Maximum Speed
Where:
K is referred to as the induced drag factor
Maximum Speed: Jet
Where:
𝜎 is relative air density
Maximum Speed: Jet
Maximum Speed: Propeller
Maximum Speed: Propeller
Take-Off Run: Jet and Propeller
The aircraft is required to clear an imaginary obstacle at the end of
the airborne section, so the take-off run includes a ground section
plus an airborne section. Based on FAR Part 25, the obstacle height
(ho) is 35 ft for passenger aircraft, and based on FAR Part 23 Section
23.53, the obstacle height is 50 ft for GA aircraft.
Take-Off Run: Jet and Propeller
Where:
CLR is the aircraft lift coefficient at take-off rotation
CDG is drag coefficient during ground run
CDoTO is zero-lift drag coefficient at take-off configuration
CLTO is take-off lift coefficient
Take-Off Run: Jet and Propeller
*The typical values
Where:
CDoLG is the landing gear drag coefficient
CDoHLD_TO is the high-lift device drag coefficient
Take-Off Run: Jet and Propeller
Where:
- CLC is the aircraft cruise lift coefficient (0.3 for a subsonic aircraft and 0.05 for a
supersonic aircraft)
- ΔCLflapTO is the additional lift coefficient (Typical values is about 0.3–0.8)
Take-Off Run: Jet
Where:
CLR is the aircraft lift coefficient at take-off rotation
µ is the friction coefficient of the runway
CDG is drag coefficient during ground run
STO is the take-off run
Take-Off Run: Jet
Take-Off Run: Propeller
Where:
𝜂𝑃 is prop efficiency
𝑉𝑇𝑂 is the take-off speed
Take-Off Run: Propeller
Rate of Climb
Based on FAR Part 23 Section 23.65. Requirements for gradient of climb as follows:
1. Each normal, utility, and acrobatic category reciprocating engine-powered airplane
of 6000 lb or less maximum weight must have a steady climb gradient at sea level
of at least 8.3% for landplanes or 6.7% for seaplanes and amphibians.
2. Each normal, utility, and acrobatic category reciprocating engine-powered airplane
of more than 6000 lb maximum weight and turbine engine-powered airplanes in
the normal, utility, and acrobatic category must have a steady gradient of climb after
take-off of at least 4%.
Rate of Climb: Jet
Where:
RoC is in ft/s or m/s
Rate of Climb: Jet
Rate of Climb: Propeller
Where:
RoC is in ft/s or m/s
Rate of Climb: Propeller
Ceiling
1. Absolute ceiling (hac). As the name implies, the absolute ceiling is the
absolute maximum altitude that an aircraft can ever maintain level flight.
In other terms, the ceiling is the altitude at which the ROC is zero.
2. Service ceiling (hsc). The service ceiling is defined as the highest altitude
at which the aircraft can climb with a rate of 100 ft/min for piston
engine and 500 ft/min for jet. The service ceiling is lower than the
absolute ceiling.
Ceiling: Jet
Where:
RoCc is rate of climb at any ceiling (altitude), and is in ft/s or m/s
𝜌𝐶 is the ambient density of air at any ceiling (altitude)
Ceiling: Jet
Ceiling: Propeller
Where:
RoCc is rate of climb at any ceiling (altitude), and is in ft/s or m/s
𝜌𝐶 is the ambient density of air at any ceiling (altitude)
Ceiling: Propeller
Parasite Drag Estimation: Jet
Parasite Drag Estimation : Propeller
