Reduction of drag and boosting of lift to drag ratio is of paramount importance to maximize flight efficiency. Body shape has a major role in producing drag. In order to reduce drag and increase lift to drag ratio I have successfully developed a new concept after spending several years to research. The concept is described below.

Background of design:- To move a body against a fluid, the body has to push the fluid sideward and pass through it. So the fluid has two moving direction with respect to body, one parallel to body’s direction and second one perpendicular to the body’s direction. Perpendicular velocity of fluid is zero until air senses presence of body. So coefficient of drag can be reduced by the way body initiates and terminates perpendicular motion of fluid with respect to body. So if we apply constant acceleration (parabolic) to initiate sideward (perpendicular) motion and constant retardation to terminate sideward motion (To gain extra kinetic energy given to fluid during sideward acceleration of air (there will be low pressure at this retarding region)).Then pressure impulse on the body will be lowest. Thus coefficient of drag will be lowest. Cycloid too can be used which has the smoothest acceleration curves and cycloid is also the curve for the fastest descent.

Using cycloid profile sideward acceleration smoothly changes from zero to peak then to zero so there would not by sudden impulses or momentum changes of fluid and sideward velocity of fluid smoothly changes from zero to peak and the to zero. This causes what’s known as 3D relieving, for example a cylinder has smooth up (y+) and down (y-) flow during a passage through a fluid. A Sphere has additional left (x+) and right(x-) flow, resulting in less velocity of flow around body and thereby less drag, this effect is commonly known as 3D relieving. Using cycloid profile for body as described in this description, you have additional smooth flow of fluid from front (z+) to back (z-) resulting in less peak velocity and average velocity of flow of fluid around body resulting in less drag. In a sense cycloid profile causes 3D reliving effect of flow of fluid from front to back of body , so velocity around body will be low resulting in less drag. While using Cycloid profile when top and bottom streamlines join vertical component of velocity will be zero so turbulence will be very less.

The Concept of Hydrodynamic Mass

When a body moves through a fluid, it must push a finite mass of fluid out of the way. If the body is accelerated, the surrounding fluid must also be accelerated. The body behaves as if it were heavier by an amount called the hydrodynamic mass (also called the added or virtual mass) of the fluid. If the instantaneous body velocity is U(t), the summation of forces must include this effect

where m_h, the hydrodynamic mass, is a function of body shape, the direction of motion, and (to a lesser extent) flow parameters such as the Reynolds number.

According to potential theory, m_h depends only on the shape and direction of motion and can be computed by summing the total kinetic energy of the fluid relative to the body and setting this equal to an equivalent body energy

The integration of fluid kinetic energy can also be accomplished by a body-surface integral involving the velocity potential.

Consider the previous example of a sphere immersed in a uniform stream. By subtracting out the stream velocity we can replot the flow as in Fig, showing the streamlines relative to the moving sphere. Note the similarity to the doublet flow. The relative-velocity components are found by subtracting U from Eqs.

The element of fluid mass, in spherical polar coordinates, is

When dm and are substituted into Equation the integral can be evaluated

Or

Thus, according to potential theory, the hydrodynamic mass of a sphere equals one half of its displaced mass, independent of the direction of motion.

A similar result for a cylinder moving normal to its axis can be computed from Eqs. after subtracting out the stream velocity. The result is

for a cylinder of length L, assuming two-dimensional motion. The cylinder’s hydrodynamic mass equals its displaced mass.

Basic concept of Aero dynamics

In an object pressure stress is acted normal to surface and shear stress acts tangential to surface. Fluid velocity at surface boundary of body is believed to be zero in viscous flow

Cycloid concept details

3.) Cycloids too can be used because they are smooth acceleration curves without any sharp bends. Equation is y=(80*((90-x)/90-(sin(2*pi*(90-x)/90))/(2*pi))) for x=1 to 90

For cylindrical body these curves can be revolved 360 degree to form front and back side of body.

In my cycloid wing design pressure at top and bottom of trailing edge is almost equal. So there is less flow around tip from bottom to top at trailing edge. This will reduce vortex generated. Thus induced drag will be very low.

Details of New concept

The molecule of fluid has to accelerate vertically to give way for body when flow is interrupted by a body then retard to remain at boundary at vertical extreme of the body. When cross-section of body starts reduce, air has to accelerate inward and again retard to remain at the boundary at trailing edge. If this change in acceleration and retardation are not smooth very high instantaneous acceleration is required for air to remain in boundary and this causes anomalies in pressure near boundary resulting in separation of flow. In the cycloid design the vertical component of acceleration of fluid molecules at leading edge starts from 0 to maximum then to 0 and then retardation starts and then to maximum retardation and then to zero at the top most part of body. Then vertical component of acceleration at trailing edge starts from 0 to maximum then to 0 and then retardation starts and then to maximum retardation and then to zero at the end of the body.

Horizontal velocity at trailing edge assures that all the kinetic energy given by moving body to air to initiate vertical velocity in air(For body to pass through)at leading edge is given back to body by air before leaving trailing edge.

Force is required to initiate vertical component of velocity of fluid molecules and impact of air molecule to body causes a vertical component of velocity in air. This continues until acceleration profile at front changes smoothly to retardation. Here pressure is low. Then cross section of body decrease and air at above initiates a downward velocity on air below due to pressure difference. This continues until acceleration profile at back changes to retardation. At this point pressure is high. At the end of retardation profile air losses its vertical component of velocity by hitting body and body gains most of the forward momentum it lost during initiation of vertical component of velocity of air at the leading edge. Due to this, stream lines at the bottom and top at the end of trailing edge is all horizontal and parallel and they do not cross each other (no crossing of upper stream line to bottom stream lines occurs) and this reduces turbulence. Since acceleration changes very smoothly from positive to negative there will be fewer anomalies in air flow near boundary. This reduces the chance of separation of flow. Anywhere near the boundary air molecules do not have to accelerate rapidly to fill the gap because of the smooth transition from acceleration to retardation through zero acceleration zones. If the acceleration curve is not smooth the air has to accelerate or retard rapidly to reach the boundary to equalize pressure. Horizontal velocity at trailing edge assures that all the kinetic energy given by moving body to air to initiate vertical velocity in air(For body to pass through)at leading edge is given back to body by air before leaving trailing edge.

We can modify the Sears Haack body based on cycloid design in such a way that cross-sectional area of the body changes smoothly as a cycloid. Equation for it is given below

y= ((80*((90-x)/90-(sin(2*pi*(90-x)/90))/(2*pi))) )^(1/2)

for x=1 to 90

Other form of Cycloid wing can be designed using cycloid as a thickness function with an appropriate camber.

Separation flow from surface of body happening at high speeds can be eliminated by plasma flow control. Thus Air will follow the cycloid body profile even at high speeds.

Even though leading edge is sharp it can be made blunt or tilt-able(So that It is always parallel to aircraft direction.) for varying angle of attack

Comparison of Aerofoil and cycloid body Profiles

Below is the animation of Cycloid body and Aerofoil wing with same length to width ratio. In animations you can clearly see turbulence is higher for aerofoil wing.( to see animation click on the image below).

Cycloid

https://www.youtube.com/watch?v=PZpI3Nf65wI

Aerofoil

https://www.youtube.com/watch?v=K1keKBh9zKY

Comparison of Aerofoil and cycloid wing

Profiles

Below is the animation of Cycloid wing and Aerofoil wing with same length to width ratio. In animations you can clearly see turbulence is higher for aerofoil wing. ( to see animation click on the image below).

Cycloid wing In this only top portion is cycloid bottom portion

is flat for wing design (for high lift to drag ratio).improved design has cycloid at the bottom

https://www.youtube.com/watch?v=OzIPtrSMbsw

Aerofoil

https://www.youtube.com/watch?v=K1keKBh9zKY

Pressure Simulation

When air hits the body vertical component of acceleration is provided by the accelerating zone of the body’s front end and this is continued until smooth transition of vertical component of acceleration of air molecules changes from positive to negative(middle portion of front end); at this portion pressure increases. After then when vertical component of air retards, pressure minimizes and body gains kinetic energy that it lost when accelerating air vertically at the front initially. You can also refer to static pressure contours of CFD results in page

Cycloid

You can Clearly see how smoothly the waves are splitting at front end. Backend can be multiple of cycloid(where in the y part of the parametric equation is multiplied b y a number).

Parabolic

1.) We can use 2 semi parabolas that are divided by their axis. First parabola with curve bending upward and second parabola with curve bending upward. The dividing point of first parabola with axis is the point of attack or front end of body. The dividing point of second parabola with axis is the mating point with body. And these two parabolas are joined tangent continuous at their other ends. Similar arrangement with another 2 semi parabolas can be used at back side of body.

2.) Another profile is similar to above except they are parabolic spirals. Polar Equation for parabolic spiral is “ r2 = 4 a θ “

Inventor: Diji N J

Nedunghayil house

Vennala P.O.

Ernakulam

Kerala

India

Ph: +91-04844063025

Mobile: +91-7736419388

Contact: delvezone@gmail.com

© Diji N J and https://sites.google.com/view/kerwingandbody2/, 2009-2017. Unauthorized use and/or duplication of this material without express and written permission from this site’s author and/or owner is strictly prohibited. Excerpts and links may be used, provided that full and clear credit is given to Diji N J and https://sites.google.com/site/hinaryprocessor/ with appropriate and specific direction to the original content.