The Science of Flight (see PDF)
& 10X and 20X Performances
THE SURFACE INTEGRAL: The science of aerodynamic lift starts with the surface integral of pressure over the surface of the aircraft. Vertical components of ΔP (surface pressure less ambient pressure) contribute to lift and the horizontal components contribute to form drag. At any point on the surface, the ratio of Lift to Drag (L:D) is approximated as 57.3 / θ, where is θ is air’s angle of attack on the surface. These concise observations identify that higher L:D can only be attained if the aircraft surface is predominantly flat (top and bottom) and flying such that those flat surfaces are 0.2 to 2.0 degrees relative to horizontal.
GENERATION OF ΔP: On lower vehicle surface positive relative pressures (ΔP, relative to ambient) product lift. Added to these are negative relative pressures on upper surfaces (integrated as -ΔP). To a first approximation, the impacting momentum of air, no-slip boundary condition, and momentum of air to resist bending downward; combine, to form these negative and positive relative pressures as illustrated by the following figure. The attached file and subsequent mathematical derivations provide further detail.
GENERATION OF ΔP: On lower vehicle surface positive relative pressures (ΔP, relative to ambient) product lift. Added to these are negative relative pressures on upper surfaces (integrated as -ΔP). To a first approximation, the impacting momentum of air, no-slip boundary condition, and momentum of air to resist bending downward; combine, to form these negative and positive relative pressures as illustrated by the following figure. The attached file and subsequent mathematical derivations provide further detail.
| thescience_of_flight.pdf |
10X and 20X Performances are Geometric Mandates!
(see pdf files at bottom of this page)
(see pdf files at bottom of this page)
Innovation Chronology - A high level of innovation is documented by patent applications from June 2019 through February of 2020.* After February of 2020, key innovations manifested in new configurations, but the true innovations (e.g. Example 3 at http://www.terretrans.com/pitch.html) could be traced to earlier models and patent specifications.
Front Tiltwing Transformation Field Prototypes - Early toy-scale prototypes demonstrated that a front tiltwing can transition from VTOL to cruising through aerodynamic forces (not actuators). Videos at https://hs-drone.com/videoshistory%2Fr%26d demonstrate this transition. VTOL and 705 transition to horizontal thrust was demonstrated (limited by thrust of tiltwing propulsors and control system to independently control that thrust).
Transformer Drone Lab Prototypes - By transforming to known, highly efficient cruising configurations, Transformer Drone can achieve the high L:D and fuel economy of those transitions. By modifying those known cruising configurations to thinner profile configurations with fences to preserve lift, even higher L:D/efficiency can be attained. This has been demonstrated through several mechanical 3D-printed prototypes that undergo that transition.
Geometric Mandate of the Towed Platform - There are laws of physics so basic, that proper application of those laws is at least as definitive as working prototypes. One example of such a law is the energy balance per the first law of thermodynamics. For aerodynamics, that law is the steady-state (constant elevation, constant velocity) force balance evaluated as the surface integral of n P dA (n is unit vector, P is pressure, dA is area) evaluated for lift (n is vertical unit vector) and drag (n is longitudinal unit vector).
This force balance taken on a towed platform approximated as a flat plate airfoil identifies that that the L:D is equal to 1/θ (one divided by theta), where θ is degrees of pitch (air angle of attack) divided by 57. This translates to a L:D of 114 at 0.5 degrees pitch. This is a geometric mandate where the primary practical constraints are on the control of flight at this low air angle of attack and design of the towed platform to perform like a flat plate airfoil. The towed platform (with a front hinge joint) passively adjusts to this steady-state θ, but instability (e.g. like a flag flapping in the wind) needs to be overcome by passive methods like damping or by active control methods.
An important artifact of this calculation is that it is a basic physics calculation as opposed to computational fluid dynamics (which relies on many assumptions and physical properties of uncertain values).
An extension of this force balance leads to the following conclusion:
A further extension of this force balance with application of an energy balance leads to best-case performances. A further extension of this force balance using typical ranges of drag coefficients leads to estimated performances of the towed platform. The primary conclusion from this analysis is:
The below two papers goes into greater detail on the calculations and range of parameters for optimal performance.
Early Commercial Emphasis - The fundamental innovation (versus operational details) has reached a plateau in early 2021 with a transition to prototyping. Initial commercial products will emphasize remote control rather than autonomous control. They include: a) kits for students and learning, b) hobby/toy transformer drone products, and c) surveillance drones for applications where speed is important and where solar power collection can extend range for hours of flight (versus minutes) and where the drone can park at remote locations as necessary to recharge.
* These dates are for Transformer Drone and SP-Drone. Innovations on the Integrated Circuit Motor and Hybrid Fuel-Electric Engines occurred from January of 2020 through January of 2021.
Front Tiltwing Transformation Field Prototypes - Early toy-scale prototypes demonstrated that a front tiltwing can transition from VTOL to cruising through aerodynamic forces (not actuators). Videos at https://hs-drone.com/videoshistory%2Fr%26d demonstrate this transition. VTOL and 705 transition to horizontal thrust was demonstrated (limited by thrust of tiltwing propulsors and control system to independently control that thrust).
Transformer Drone Lab Prototypes - By transforming to known, highly efficient cruising configurations, Transformer Drone can achieve the high L:D and fuel economy of those transitions. By modifying those known cruising configurations to thinner profile configurations with fences to preserve lift, even higher L:D/efficiency can be attained. This has been demonstrated through several mechanical 3D-printed prototypes that undergo that transition.
Geometric Mandate of the Towed Platform - There are laws of physics so basic, that proper application of those laws is at least as definitive as working prototypes. One example of such a law is the energy balance per the first law of thermodynamics. For aerodynamics, that law is the steady-state (constant elevation, constant velocity) force balance evaluated as the surface integral of n P dA (n is unit vector, P is pressure, dA is area) evaluated for lift (n is vertical unit vector) and drag (n is longitudinal unit vector).
This force balance taken on a towed platform approximated as a flat plate airfoil identifies that that the L:D is equal to 1/θ (one divided by theta), where θ is degrees of pitch (air angle of attack) divided by 57. This translates to a L:D of 114 at 0.5 degrees pitch. This is a geometric mandate where the primary practical constraints are on the control of flight at this low air angle of attack and design of the towed platform to perform like a flat plate airfoil. The towed platform (with a front hinge joint) passively adjusts to this steady-state θ, but instability (e.g. like a flag flapping in the wind) needs to be overcome by passive methods like damping or by active control methods.
An important artifact of this calculation is that it is a basic physics calculation as opposed to computational fluid dynamics (which relies on many assumptions and physical properties of uncertain values).
An extension of this force balance leads to the following conclusion:
- Drag on the flat surfaces of the towed platform actually decreases with increasing velocity (versus increasing with velocity squared) for fuselages and many wings; this translates to the towed platform being particularly conducive to higher-velocity flight.
A further extension of this force balance with application of an energy balance leads to best-case performances. A further extension of this force balance using typical ranges of drag coefficients leads to estimated performances of the towed platform. The primary conclusion from this analysis is:
- The key parameter that locks in highly efficient performance of the towed platform is a light specific load on the platform. This would be a specific load of 0.5 to 20 lb/ft2 in the widest range case; that load is highly dependent on both velocity and ambient pressure.
- A method to minimize the specific load is to evenly distribute a load (e.g. solar cells, fuel cells, batteries) on a sheet/board stretched between a frame (sides and edges) of the towed platform.
The below two papers goes into greater detail on the calculations and range of parameters for optimal performance.
Early Commercial Emphasis - The fundamental innovation (versus operational details) has reached a plateau in early 2021 with a transition to prototyping. Initial commercial products will emphasize remote control rather than autonomous control. They include: a) kits for students and learning, b) hobby/toy transformer drone products, and c) surveillance drones for applications where speed is important and where solar power collection can extend range for hours of flight (versus minutes) and where the drone can park at remote locations as necessary to recharge.
* These dates are for Transformer Drone and SP-Drone. Innovations on the Integrated Circuit Motor and Hybrid Fuel-Electric Engines occurred from January of 2020 through January of 2021.
| force_energy_analysis.pdf |