Performance

Aircraft data (update all tables and graphs after having fixed all dimensions)

The plane performance is studied with all the available information. For this calculations, all dimensions must be stated first and all formulas are referenced to the first dimensions so when a single value is changed, like the cruise speed, the wingspan of the horizontal stabilizer or the fuselage shape, all the graphs and charts change in accordance.

Airfoils
Two airfoils are chosen for the wing and the horizontal stabilizer. The wing airfoil chosen is the Eppler E374, copying the airfoil of Reaper-like glider model studied before in similar aircrafts. These type of airfoils use the Eppler code, designed by Professor Richard Eppler based in some methods used in computational fluid dynamics for low Reynolds numbers.

“Professor Richard Eppler is a pioneer in the field of computational aerodynamics. He wrote his first codes using punched paper strips, the high speed main memory at these times was a magnetic drum, which could hold several bytes.

Eppler developed a very fast and elegant design method, based on conformal mapping, which is the heart of his computer code. Because an airfoil also has to operate outside of its design point(s), a fast integral boundary layer method and (for the analysis of given airfoils) an accurate third order panel method (parabolic velocity variation) was added. Furthermore the code offers possibilities to modify the geometry, to calculate drag polars, and various plotting options. Due to its early roots, the computer code has been developed as a batch code. Textual and graphical output is directed to files, which makes the FORTRAN 77 code easily portable and system independent. On the other hand, the input files are quite cryptic and hard to handle for beginners. The elaborate description of theory and code [Eppler, R. and Somers, D.: A Computer Program for the Design and Analysis of Low-Speed Airfoils, NASA TM-80210, 1980] even contains an (now outdated) version of the FORTRAN-IV program.

The strength of the code is the design part and the fast analysis part, which makes it very well suited for the design task. The results of the integral boundary layer method agree astonishingly well with experiments, if the Reynolds numbers are above 500'000. The design module can be used to design very smooth airfoils shapes, including the leading edge region, which is often difficult with other codes. On the other hand, the design method is quite abstract and difficult to handle for beginners.

The boundary layer analysis is performed using the calculated, inviscid (without friction) velocity distributions as input; there is no direct coupling between boundary layer flow and the external flow field. Transition prediction is performed by testing the boundary layer parameters against a set of empirically derived transition relations, which work quite well for attached flow in a wide range of Reynolds numbers.

In the low Reynolds number regime the results are usually not very accurate if a laminar separation bubble or larger separated flow regions occur. This is a result of the integral boundary layer method, which simply cannot model separation (this would require some sort of coupling between boundary layer analysis and the calculation of the external flow). The code has a option to perform a displacement iteration in order to take the displacement effects of the boundary layer into account, but there is no direct interaction, as, for example, in Xfoil. Recent (2007) additions to the code however, are an improved model of laminar separation bubbles and turbulent separation. The code itself is available for a fee directly from Prof. Richard Eppler in Germany or from his US distributor Dan Somers.”

http://www.mh-aerotools.de/airfoils/methods.htm
also: http://www.pdas.com/eppler.html

Max thickness 10.9% at 34.3% chord. Max camber 2% at 38.9% chord

http://airfoiltools.com/airfoil/details?airfoil=e374-il
Performance graphs to be updated with Re number and high N critic

The horizontal stabilizer has a symmetric airfoil and one of the simplest and most used in slow planes, the NACA 0012, with 12% thickness at the 30% of the chord. The plane doesn’t need too much lift in the tail, forces will be balanced by the angle of attack of the airfoil.

http://airfoiltools.com/airfoil/details?airfoil=n0012-il
change Re

The NACA 0012 is used in the vertical stabilizer too for the same reasons.

CAD modelling with Siemens NX 9

It is time to create the first model of the airplane with all the considerations taken before.
The surface of the fuselage is going to be created with two main sketches, horizontal (plan XY) and vertical (plan YZ). To find the intersection of these parallel plans with the sketches of the fuselage, vertical and horizontal straight lines are needed for creating intersections that will be start points.  Then they will be united with curves drawn along parallel plans along the longitudinal axis Y so it will be formed by several sections, each section formed by 4 curves surfaces or fuselage plates. As it is symmetrical along axis X, just one curve is needed on each side and section, the symmetry will be applied later.

The two sketches are united by 7 section curves

Front view of these sections

All sketches and section curves conform the fuselage divided in 6 main parts (24 in total)

Wing and tail are added (still without proper airfoils). Shark fin design is aesthetic, as it could be the wing with sweep angle and winglets, but harder to build.

Side view of design 0.2

It can be appreciated that even with a high wing, the downwash may affect the tail. The fuselage may also affect the vertical stabilizer.

 Interior of the fuselage with main components placement along longitudinal axis.

Isometric view of design 0.3

Main landing gear, propeller, camera and gimbal are built. The ailerons take form. The landing gear still doesn’t protect the camera in case of collision.

Landing gear detail without bearings. Rigid rods transmit forces to fuselage and wing. This camera has its own WiFi antenna

Camera and gimbal detail. It is a 3 axis gimbal with 3 brushless motors. Pitch control covers from -130° to 90° and rolls from -45° to 45°.

Fuselage side cut

From the front to the rear, the gimbal is embedded in the fuselage upwards to protect more the camera from possible crashes. It will be glued or screwed to the main structure, with a big enough hole allowing the free movement of the gimbal system. Then the battery is placed just below the wing and as low as possible. The battery is going to feed the motor through the ESC and the servos through the BEC system of the ESC, which controls that a small amount of the battery is given with proper voltage to the servos’ motors. The battery and ESC must be placed next to each other, but the ESC must be placed a bit to the rear too to reach not only the servos of the wing but those in the tail too. Between the servos and the ESC, a gyro system circuit board is supposed to control the surfaces to compensate turbulences and unexpected wing forces that disturb the plane’s flight, so extension cables might be needed to reach the servos. The further back these components are placed, the better, because there is already a lot of weight from the camera in the front.

This scheme of the Ranger Ex Platform gives an idea of a more detailed study of the components relative position:

http://www.getfpv.com/planes/fpv-planes/volantex-ranger-ex-757-3-pnp.html

The following designs of the plane have all improvements of its parts, either for making it more realistic, efficient or easier to manufacture.

The landing gear is put a bit forward to protect the camera. The single wheel is added to the back of the plane to complete de landing gear. The propeller and motor models are improved, as well as the gimbal and the union between main fuselage and the tail. Other bodies changed from solids to surfaces for a first fluid simulation.

Side view of design 0.4

The airfoil E374 conforms the detailed wing structure. The coordinates for this airfoil are taken from airfoiltools.com and plotted as a spline in NX, then extruded. The ailerons are formed almost at the tip of the wing with a rib of separation from the edge. There are two thin rods that connect the ailerons to the wing and allow their independent rotation around it.

One-piece E374 wing with ailerons and rounded edges

Aileron hinge detail

The horizontal stabilizer uses a symmetric airfoil, the NACA 0012.

Just as the wing is made, the horizontal stabilizer is built

The vertical stabilizer changes to a more common shape which is stronger, easier for manufacturing and controlling the yaw movement. For the moment it still has a symmetric cut but not a formalized airfoil, just straight lines and arcs at the front. The thin rod inside joins the rudder surface to the stabilizer, allowing it to freely rotate around it.

 Vertical stabilizer side view

The next design has a formalized landing gear structure. The main landing gear is designed according to existing wheels and mounting, as well as the tail connection, all of them available at local stores.
A new propeller is used now, with much more aerodynamic and realistic blades modelled in 4 quarters out of splines, tangent on the front and rear plans.
The wings are cut in two, the same way they will be manufactured and mounted on the plane, one attached to each side of the top fuselage. Their tips are flattened to follow the shape of the tip rib and the holes for the rod are correctly made to sew all the surfaces together.
The fuselage part joining the front and the tail is removed and replaced by a long and strong rod.

Isometric view of design 1.1

Formalized main landing gear

Formalized tail landing gear

10x6 inches propeller blades

All remaining solids are turn to surfaces with some remodeling. The motor is pulled back, out of the fuselage, and installed in a mount. The main wheels bearings are improved.

Motor mounting

Landing gear detail

There is one issue with the propeller and it is the fuselage that blocks the inlet air to the bottom part of the propeller, so that part will have its thrust reduced. A simple solution is to open holes in the foam that work as air inlet, taken from the uniform current directly to the propeller blades. The rigid structure of the back of the fuselage will be weaker but he motor will push more.

Although the structure has aerodynamic efficient curves, the available machines can’t cut that way, they just can approximate the smoothness with several straight lines.

    

                 

The fuselage must be optimized for manufacturing. The hot wire 4-axis cutting machine cuts the foam block in straight lines because the wire is tense and such is the way it is modelled now. This design includes an FPV camera too, apart from the camera mount below the fuselage, and it will be located at the foremost part of the fuselage to create a cockpit environment. The plastic cover protects the camera in case of crash and reduces the drag with the air flow.

 

             Example of a nose with a big camera and a plastic case

http://www.hobbyking.com/hobbyking/store/__38072__HobbyKing_174_8482_Go_Discover_FPV_Plane_EPO_1600mm_PNF_.html

Again, from scratch, two main sketches are made, horizontal and vertical. The plant shape must be wide not only to hold the components such as the battery, 50 mm wide, but to have wide walls of foam that give strength to the plane. At the nose of the plane, a hemispherical shape is needed to place the cover of the FPV camera. It will have big enough dimensions to hold, in case of need, one of the biggest cameras considered and a pan/tilt mechanism.

XY sketch

The top line of the vertical sketch is the most critical. Its shape has big repercussions on the total drag of the fuselage. The last version of the fuselage had 635 mm of length. Taking out the peak of the nose and the rounded back that is not properly manufactured in the simulation, the length is 600 mm, easily divided in parts of 200 mm. Once the configuration is fixed for 3 blocks with the same width, the angles of the straight lines are set with the help of the shadow from the previous fuselage to be as similar as possible and a reference arc in red which gives an approximate shape of the smoother lines that help the air flow stay close to the plane and not to become detached. If these vertices are too sharp the plane will need a more powerful motor.
The bottom lines are made tangent to the camera cover too and adjusted to join the middle rod of the fuselage. Being straight help the fixation with the landing gear and the gimbal.

YZ sketch. Red arc is tangent to the air flow and camera cover.

Then the transversal sketches join the two sketches through the intersections of those with the plans, creating the side shape of the blocks that the wire will cut.

XZ sketches

Thanks to the sketches the surfaces are created one by one, simpler than before, and made symmetrical. The rest of the fuselage is formed by the union rod and a small part at the rear that will hold the tail elements.

Isometric view of the fuselage design 1.4

Adding the main parts completes the configuration.

Isometric view of design 1.4 with main parts.

Detailed configuration

The main parts of the plane are dimensioned and positioned according to numerous factors such as structural strength, aerodynamic efficiency, security and stability. The final part is the optimal configuration for this kind of mission and this payload.
To place the components first it is important to know how much do they weight. The heavier components are the battery (600 g.) and the camera (335 g). The weights are taken with the most restrictive component specifications (weight and dimensions) so in case the components are changed to other dimensions, they will just leave free space in the fuselage and reduce maximum take-off weight. If the plane in the end is too light the easiest option is to reduce wingspan. According to this, the design of the wing, fuselage, tail, motor and landing gear begins.

Plant sketch of the plane with the position of the main electronic components

Wing

The wing, to begin with, is slender (aspect ratio = 12.5) for improving gliding flight. Similar to other planes, it has a wingspan of 2500 mm and a main chord of 200 mm. Choosing later a proper airfoil will state its thickness. For manufacturing purposes it is straight and rectangular, without dihedral angle and no sweep angle because it won’t be affected by compressibility effects. The only control surfaces it will have are 400 mm ailerons in each tip, not too wide because they are far from the center of gravity, so a little movement will create enough momentum.

Referred to the vertical position, the wing is on the top of the fuselage. This way it leaves free space below for the electronic components, has better aerodynamic efficiency (free extrados and less fuselage interference) and reduces ground effect that may difficult take-off and especially landing.

The battery will be placed below the wing, to increase stability, so when the wing lifts the plane, the center of gravity will be as near as possible to the center of lift and below. If the wing suffers from slipping by the airstream it tends to auto-stabilize, however it might suffer from Dutch roll (negative dihedral may be needed to reduce this effect).

In case of crash, which is very likely to happen, the wing won’t be as much affected as the fuselage. In this case it is preferable that the foam from the fuselage absorbs the impact with the ground or with a wall/tree because the wing surface will be weaker (plastic film) or more fragile (wood board). In addition the foam is cheaper, easier to get and can be repaired as a puzzle with some glue.

The horizontal position along the fuselage centerline is set between ¼ and ½ of the length, measured from the nose. This is caused by the second heavier element, the camera and the gimbal. This group has extra constraints: it must be at the foremost part and below the fuselage for evident reasons of field of view. The fuselage shouldn’t appear on the screen and the lens should cover the field from the horizon to at least 60 degrees downwards. 

Now the distance from the camera to the wing is crucial. The closer they are, the less weight will be compensated in the tail, but if they are too close they create such a low momentum that the tail will make the plane pitch up.

Motor

The motor has a pusher propeller with two blades, it pushes the plane structure forward from behind the wing. This configuration makes a more complicated fuselage shape but it is the most efficient for this mission. The reasons that have led to this configuration are as follows:

The motor can’t be placed in the front as a tractor because it will result in weight problems, risk of breaking propellers when frontal crash and it will cover the view of the camera.

It can’t be placed in the rear because of the weakness of the tail (vibrations may harm the structure due to fatigue), the closeness to the ground, the long distance from the battery and the weight balancing too. The negative stability would be hard to control too, because the center of gravity would be much further from the motor, contrary to tractor motors that auto-stabilize. Furthermore, the shaft works better if it has a compression force.

Front motor and rear motor

So the best option is to place it in the middle, as close as possible to the center of gravity and lift (close to the battery and the wing). Vertically it is placed at the same height as the wing, to give the propellers more space to rotate freely and to create less momentum among the wing line. Setting it to the centerline of the fuselage could be possible but very difficult, the fuselage might be split into a twin-boom fuselage which is harder to manufacture.

A problem to deal with is the turbulences the airstream from the motor creates backwards. If the motor is placed before the wing it might give it extra lift explained with the Coandă effect, as seen in planes like the Boeing YC-14 or the Antonov An-72, but placing it behind is more spread.

Boeing YC-14 and Antonov An-72

http://s163.photobucket.com/user/hawkeyes_bucket/media/Real%20Aircraft/fly14.jpg.html

http://www.theaviationzone.com/images/russian/an72/bin/an72_07.jpg

The motor behind the wing may be affected by its trail or even improve the air circulation but being at the top height decreases the interaction with the fuselage and tail, as well as avoiding the ground in a collision.

Fuselage

The fuselage is constrained by the payload and the wing and motor configurations, as it works like a structural union between parts, and it should have the lowest wetted area possible to reduce drag. Having pointed shapes is not very important for this mission as flight speed won’t be over 0.2 Mach. Although it helps reduce drag, the nose cone needs to be rounded to absorb crashes and wide to hold the camera.

Around the motor, the fuselage must be strong to stand its vibrations and forces pushing the structure, but not too wide because the motor needs fresh air to pass through its propeller. In a more detailed design the fuselage might need air intakes like reversed fish gills or just holes, not just for air intake but for cooling the motor (keeping it below 60 °C if possible).

The shape doesn’t need to be cylindrical because it won’t be pressurized. The sections have elliptical cuts and between them the side line is as straight as possible, so manufacture will be easier. The most demanding section in terms of structural integrity is the middle of the fuselage, next to the motor cowling. It is as narrow as possible to let air flow through the propeller and it has abrupt curves. Manufacturing simulation may cause this part to change and improve.

Fuselage side sketch

Tail

The horizontal stabilizer is rectangular too, for the same reasons as the wing. It has a wingspan on 500 mm and a main chord of 120 mm. The elevator surface covers almost all the wingspan and is wide to compensate a possible downwash and turbulence effect caused by the wing trail. The configuration is fixed by the rest of the plane, because the rear part gets the turbulences the front parts create. To avoid the wing downwash and propeller stream the horizontal stabilizer is placed as down as possible and as far as possible, to give pitch momentum too. The vertical stabilizer is large as it will get some of the turbulent flow so it also has a long and wide rudder. Further fluid analysis will tell if the vertical stabilizer can keep its original configuration (A-1), change to a B-1, with two small vertical stabilizers in each tip of the horizontal stabilizer, or a V tail (or butterfly tail). In these cases the rudders will need two servos and a bit more complex control.

Landing gear

A fixed landing gear is considered because the flight speed won’t create such a high drag on the wheels to impede normal operation.

The chosen type is the conventional mainly because of the camera placement, it wouldn’t allow a front wheel in the nose, or the main landing gear would be difficult to place back if there is a high wing.

The main two wheels are placed as close to the camera as possible to create a protection between the nose and them, so in a typical crash the camera would be covered from impact. Although the camera will be covered, in a bad landing the plane might flip over if the landing gear brakes too hard, the wind is not favorable or the pilot is unexperienced.

Also the impact is transmitted to the foam and the wings, partially absorbing the force. Crash test will be made with finite element method simulation and stress analysis.

Other similar planes are found to have a very similar fuselage shape. The examples are:

Volantex RC Ranger EX

http://www.volantexrc.com/product/ranger-ex-757-3

Volantex RC FPVRaptor V2

http://www.volantexrc.com/product/757-v2-fpv-raptor-v2

Skywalker 2014 edition

http://www.fpvmodel.com/latest-version-skywalker-2014-1800mm-fpv-rc-plane_g6.html

3DRobotics aero

https://store.3drobotics.com/products/3DR-Aero

ICON A5 (manned aircraft)

http://www.iconaircraft.com/photo-gallery-flight-test-3.html