V-n Diagram
Dive, Stall, and Cruise Speed
In the V-n diagram analysis, the aircraft stall speed was determined to be 61 KEAS (Knots Equivalent Air Speed)(or equivalently 113 km/h) as described previously in the initial requirements. Similarly, it was previously specified that the aircraft's cruise speed would be 150 KEAS (277.8 km/h). Using these equivalent airspeeds, the never exceed dive speed can be determined using the following equation:
Substituting the 150 KEAS cruise speed into the equation resulted in a dive maximum velocity of 225 KEAS (416.7 km/h). It is also important to note that the base units used for this analysis were feet per second in order to comply with the various empirical formulas used in the analysis. The analysis also utilizes International Civil Aviation Organization (ICAO) standard atmosphere at sea level. In this condition, air density was assumed to be 1.225 kg/m3 assuming perfectly dry 15C air at sea level [1].
Stall Limit
The stall limit is important to highlight the design capability limit of the aircraft for safe operation. It also allows for designers to see what kind of loading would need to be considered for the aircraft structures. The stall limit could be calculated as follows:
Where CLMax was assumed to be the maximum lift coefficient with all of the flaps deployed. This maximum lift coefficient was 2.498 which resulted in a stall speed of 61 KEAS. As stated earlier, the density was assumed to be at standard sea level as described in the ICAO which is 1.225 kg/m3. This resulted in the following equation for the stall loading curve. The slope was also described in the negative direction in order to limit the negative loading limit. It is also important to note that the density and velocity is denoted with an infinity subscript to represent the far-field density and velocity respectively. These values represent measurements taken from a distance away from the aircraft where no disturbances occur.
Load Limits
The maximum and minimum loading was determined assuming that the aircraft would be classified as utility category aircraft. By following this assumption, the aircraft's maximum structural load limit was determined to be 4.4 as described in the AWM 523.337 [2]. From the same manual, it was also determined that the aircraft would have a negative manoeuvering structural load of 0.4 times the positive load factor. This resulted in a lower structural load factor of -1.76.
Alternatively, had the aircraft assumed a commuter category requirement, the following formula would have been required to determine the maximum positive load factor.
Provided that the aircraft weight was 8767.5 lbs, the n+max would result in a maximum positive structural load of 3.38. Following the same guideline for maximum negative loading, would result in a load factor of -1.35.
The utility category was chosen for this aircraft since this aircraft is expected to be able to withstand higher loading. This is especially important for a VTOL aircraft that may experience harder landings and experience more harsh weather conditions. This was especially true considering the regions the aircraft is designed to operate in such as the Canadian coast and islands.
Gust Loads
The gust loading line is highly critical to calculate and take into account as it can be greater than the maximum positive or negative structural limit. The gust may bring the structural limit beyond the previously predetermined maximum values. This is important as this indicates that some structural safety factors must be taken into account for safety purposes. The probability of the aircraft experiencing the specific gust and airspeed velocity combination at the same time is low but it can be possible. The gust loading lines were calculated using the following formula:
Note that the formula is describing a change in loading. In this analysis, the initial loading was assumed to start at a steady level flight which is represented with n=1. In this equation, CL∝ represents the slope of the linear part of the lift versus the angle of attack curve. On the other hand, U represents the instantaneous gust velocity which must be alleviated with a constant in order to take into account the fact that real gust intensity behaves like a sinusoidal wave. U can be calculated as follows:
Where K represents the previously discussed alleviation factor which can be calculated with the following formula:
In this equation, µ represents the mass ratio which can be calculated as follows:
In this equation, the mean aerodynamic chord length of the wing is denoted as \(\bar{c}\) and CL∝ represents the lift curve slope. Ude was determined to be 30ft/s for the dive and 50ft/s for the cruise portion. These values were determined using Figure 14.5 of Raymer as seen in Figure 1 below.
Figure 1, Equivalent gust velocity Ude [1].
The maximum gust velocity of 30 ft/s for the cruise was chosen in order to allow the aircraft to be more rugged in the environment it will be flying in. This has also been the standard value for most aircraft as described by Raymer [1].
V-n Diagram
Figure 2, V-n Diagram for the aircraft "Niska" depicting the maximum load factor it can possibly experience in its lifetime.
Discussion of V-n Diagram
The V-n diagram for 'Niska' was reasonable for the size of the aircraft. The aircraft would be designed for a considerably higher loading than commuter standards since the aircraft operation is unique. First, the aircraft is a VTOL concept with amphibious operation capability. This meant that the aircraft should be able to withstand higher landing loadings as well as loadings created by gusts on open water. It can also be noted that the gust lines do not affect the aircraft's outer envelope as the aircraft is considerably heavy for its wing size.
References
[1] D. Raymer, Aircraft Design: A Conceptual Approach, Sixth Edition. Washington, DC: American Institute of Aeronautics and Astronautics, Inc., 2018.