Early Afternoon Concurrent Panel Sessions: Commercial Space Industry Snapshot: Presentation: Small Catapult-Assisted Horizontal-Launch Reusable RBCC SSTO Spaceplane for economical short-duration LEO access

This article discusses the conceptual design, flight trajectory calculations, and utilization of the possible future horizontally-launched reusable Single-Stage-to-Orbit (SSTO) spaceplane for small payload short-duration manned/unmanned access to Low-Earth-Orbit (LEO). The 10,000 lb spaceplane would use 5,000 ft catapult-assist horizontal-launch facility and conduct powered approach and landing on conventional horizontal paved runways following the gliding atmospheric re-entry. To increase the economy of operation, the launch facility located at high elevations (4,000+ ft) equatorial region is required, such as, the plateaus in Kenya and Tanzania in Africa and/or Ecuador in South America. A 500-lb payload, including pilot-commander, is envisioned. The propulsion cycle is a Rocket-Based Combined Cycle (RBCC) turbo-ram-rocket design that provides optimistic 1,000 sec average specific impulse with LO2 (rocket mode only) and requires high-energy-density fuel of combined specific impulse of Isp=700 sec. Ablation materials are used for re-entry cooling, however incurring high weight penalty. The 3g catapult-system with the average launch power of 20,000+ HP represents the zeroth-stage significantly increasing the transportation efficiency while enabling the SSTO design. Catapult system would be able to accelerate the spaceplane to high transonic speeds followed by the supersonic turbo-ram 2g max-Q climb initiated after sufficient altitude is gained. The 12,500 lb thrust rocket propulsion mode initiated at about 200,000 feet and M=5 accelerates the spaceplane into the 200-km prograde LEO. Powered flight lasts about 6 minutes followed by coasting and orbit acquisition. Thrust vectoring for attitude control and orbital maintenance/maneuvers is conventional using thrusters with monopropellants. Dynamic differential equations incorporating global ISA model, atmospheric drag, thrust changes, and active pitch and roll steering maneuvers for orbit injection are integrated using Ordinary Differential Equations (ODE) numerical solvers. Some of several possible uses of this small-payload spaceplane is in assisting space junk removal, transportation, and mini satellite deliveries

Optimization of Takeoffs on Unbalanced Fields using Takeoff Performance Tool

Unbalanced field length exists when ASDA and TODA are not equal. Airport authority may add less expensive substitutes to runway full-strength pavement in the form of stopways and/or clearways to basic TORA to increase operational takeoff weights. Here developed Takeoff Performance Tool is a physics-based total-energy model used to simulate FAR/CS 25 regulated airplane takeoffs. Any aircraft, runway, and environmental conditions can be simulated, while complying with the applicable regulations and maximizing performance takeoff weights. The mathematical model was translated into Matlab, Fortran 95/2003/2008, Basic, and MS Excel computer codes. All existing FAR/CS 25 takeoff regulations are implemented. Average forces are calculated for takeoff accelerate-go and accelerate-stop scenarios with all-engine-operating and one-engine-inoperative conditions. Special attention was paid to simulating increase in FLLTOW as the clearways and/or stopways are added in varying ratios. From the limited parametric study it appears that clearway-to-stopway ratio addition of 4:1 gives good overall performance increase while keeping decision/action speed constant. The critical clearway length exists for which both TORA and TODA are equally limiting. Corrections for effective runway slopes and wind were derived. The presented takeoff performance model provides a platform for more in-depth optimization studies and economic analysis of runway-airplane-engines synergy

On Atmospheric Lapse Rates

We have derived and summarized and most important atmospheric temperature lapse rates. ALRs essentially govern vertical atmospheric air stability and creation of some cloud types. The sensitivity analysis of various atmospheric lapse rates and their dependence on actual ideal-gas air properties and gravitational attraction was conducted for the first time to the best of our knowledge. SALR, which has DALR as the upper asymptote, showed steepest decrease at around 9 degrees Celsius then flattening out and apparently approaching another asymptotic solution which has not been investigated as it falls outside of the terrestrial temperature range. ISA lapse rates are adopted atmospheric standards and hence do not depend on actual conditions. We have also analyzed the dependence of DPLR on air temperatures and moisture content. Understanding thermodynamics and dynamics of atmospheric moist air and phase transitions is of fundamental importance for safety and economy of flight operations and aircraft performance

Long and short-range air navigation on spherical Earth

Global range air navigation implies non-stop flight between any two airports on Earth. Such effort would require airplanes with the operational air range of at least 12,500 NM which is about 40-60% longer than anything existing in commercial air transport today. Air transportation economy requires flying shortest distance, which in the case of spherical Earth are Orthodrome arcs. Rhumb-line navigation has little practical use in long-range flights, but has been presented for historical reasons and for comparison. Database of about 50 major international airports from every corner of the world has been designed and used in testing and route validation. Great Circle routes between many major international airports have been generated and waypoints designed for both GC and rhumb-line routes. Some global-range flights including to polar crossings and/or long flights over open water with not many alternate landing sites available may be ETOPS limited. Additionally, we summarized short-lines navigation theory with particular emphasis on Polar Regions and very short distances elsewhere on the Earth. Working equations and algorithms have been coded into several high-level programming languages, such as, Fortran 90/95/2003/2008, Matlab, and True Basic. Considerable testing of programs have been conducted and compared with the publicly-available geodesic computations over the surface of the terrestrial reference ellipsoid. Distance computations usually were no more than 0.3% in error, while the angles and courses discrepancies were mostly within few angular minutes. Further development will include computations of gliding distances from any altitude under arbitrary winds depending on the type of aircraft and the calculations of PET and PNR for every segment of the route and arbitrary wind conditions

A Contribution Toward Better Understanding of Overbanking Tendency in Fixed-Wing Aircraft

The phenomenon of overbanking tendency for a rigid-body, fixed-wing aircraft is investigated. Overbanking tendency is defined as a spontaneous, unbalanced rolling moment that keeps increasing an airplane’s bank angle in steep turns and must be arrested by opposite aileron action. As stated by the Federal Aviation Administration, the overbanking tendency may lead to a loss of control, especially in instrument meteorological conditions. It was found in this study that the speed differential over wing halves in horizontal turns indeed creates a rolling moment that achieves maximum values for bank angles between 45 and 55 degrees. However, this induced rolling moment may already be a part of other lateral-directional stability derivatives, most probably in dihedral effect. Nevertheless, the overbanking tendency may also be induced by propulsive and/or gyroscopic moments, airplane and flight control rigging problems, human factors, and improper piloting techniques. Straightforward explanation of the overbanking tendency is based on the asymptotic spiral divergence lateral-directional mode, which is very common in many FAR 23 airplane designs. The full nonlinear stability model, which may include coupling of longitudinal, lateral, and directional motion in steep turns at high angles of attack and including propulsive moments, may be required to make the final judgment about the existence of the overbanking tendency. A thorough review of airplane turning performance in horizontal plane is presented

Modeling and Computation of the Maximum Braking Energy Speed for Transport Category Airplanes

Transport-category or FAR/CS 25 certified airplanes may occasionally become braking energy capacity limited. Such limitation may exist when heavy airplanes are departing airports at high-density altitudes, on relatively long runways, and/or possibly with some tailwind component. A maximum braking energy VMBE speed exists which may limit the maximum allowable takeoff decision/action speed V1. The ever-existing possibility of high-speed rejected takeoff in such conditions may also limit the airplane gross weight for declared available distances. To gain deeper insights and acquire better understanding of the topic, a theoretical model of the maximum braking energy and the related VMBE speed for T-category airplanes was developed. The total kinetic energy of an airplane includes translational and rotary kinetic energy and the potential height-energy component for sloped runways. Time-dependent airplanes’ mechanical power expression has been derived. Weight transfer during dynamic braking has been implemented in the full nonlinear model. Added mass due to rotary inertia of spinning components has been incorporated and assumed constant. The brakes thermal model is based on a lumped-parameter analysis of ventilated brake rotors and stators; the thermal model is based on a small Biot-number approximation and sufficiently well describes the physics of friction braking. The nonlinear differential equations of motion and the differential thermal model are coupled. A nonlinear model incorporating a set of ordinary differential equations with tire slip can be solved numerically. This model enables determination of the entire history of translational and angular accelerations and speeds, longitudinal distance, forces, torque, and disc temperature during braking. A simpler model assuming constant physical and thermodynamic parameters is solved analytically for constant negative acceleration. This linear analytical model has been used as a workhorse method in our calculations. A new semi-empirical expression of temperature-dependent friction coefficient on brake rotor-stator pairs has been proposed. A theoretical model of maximum braking energy speed VMBE, which includes density-altitude, runway slope, and wind effects as parameters, has been developed for the first time to the best of our knowledge. A comparison of the theoretical VMBE model showed good agreement with measured and approved data for the B737-400 airplane at different density altitudes with and without, individual and combined, runway slope and tailwind effects. Results for new and fully worn brakes were obtained showing the effect of elevated temperatures on brake fade and consequently braking time and distance

A total-energy based model of airplane overspeed takeoffs

A novel total-energy model of overspeed takeoffs is introduced . The mathematical model is based on the 6-DOF rigid-body aircraft equations of motion during takeoff and initial unaccelerated climb. Procedures and calculation steps to determine final takeoff weight and improved takeoff speeds are explained and discussed. A particular example was solved to demonstrate its potential use. A novel diagram for quick and easy determination of improved-V2 parameters was designed. Overspeed or improved-V2 takeoffs are very important safety and economic tool in scheduled airline operations. Unfortunately, overspeed takeoffs are not well understood or used as frequently as possible in practice. The main goal of this article is thus intended to be a contribution toward a better understanding of overspeed takeoffs as well as for fast estimation of relevant parameters. The equations and algorithms presented could be easily programmed in any low- or high-level computer language and used in airplane performance computers, print and digital databases, or onboard avionics

High-elevation equatorial catapult-launched RBCC SSTO spaceplane for economic manned access to LEO

A conceptual and feasibility study of an RBCC SSTO catapult-launched reusable strap-on parallel-boosted gliding-reentry lifting-body spaceplane for economic manned short-duration 300-kg payload LEO access is presented and discussed. One or more high-elevation equatorial spaceports are proposed each having magnetic-levitation catapult-launch mechanisms for subsonic to supersonic launches, adjacent paved runways, and on site facilitates to produce cryogenic propellants. High-elevation equatorial launch sites provide less dense atmosphere, less distance to LEO, and the possibility to launch into any orbital plane. The launch window for zero-inclination direct equatorial orbits requiring minimum specific energy and providing maximum specific payload capability of any existing launch system is continuously open and rendezvous opportunity frequent. Combined equatorial catapult launch and high-altitude facilities propulsion reduces energy requirements by about 500-600 m/s making it perhaps the most efficient future terrestrial launch system. Additionally, the use of airframe-integrated ramrocket RBCC engine further increases specific impulse for the portion of transatmospheric flight thus further reducing propellant requirements. Due to the fact that the proposed spaceplane is relatively small, the technical, organizational, and safety requirements are much relaxed. Substantially lower operational cost are expected per flight. The first cost analysis suggests about $3,000/kg for payload to LEO. The fact remains that SSTO is a very marginal concept and that RBCC engines still need flight test proving. Without more energetic propellants and very efficient RBCC propulsion devices perhaps in combination with air launches or terrestrial catapult launch facilities there seems nothing on the horizon that could make SSTO concept truly practical

Global Optimized Isothermal and Nonlinear Models of Earth’s Standard Atmosphere

Both, a global isothermal temperature model and a nonlinear quadratic temperature model of the ISA was developed and presented here. Constrained optimization techniques in conjunction with the least-square-root approximations were used to design best-fit isothermal models for ISA pressure and density changes up to 47 geopotential km for NLPAM, and 86 orthometric km for ISOAM respectively. The mass of the dry atmosphere and the relevant fractional-mass scale heights have been computed utilizing the very accurate eight-point Gauss-Legendre numerical quadrature for both ISOAM and NLPAM. Both, the ISOAM and the NLPAM represent viable alternatives to ISA in many practical applications and specifically for drag calculations at high altitudes for trans-atmospheric flight vehicles. A particular advantage of ISOAM and NLPAM is that only single expressions for each: temperature, pressure, and density is used compared to multiple different expressions in multi-layered ISA formulation. A parabolic NLPAM is an especially accurate replacement for ISA up to 47 geopotential km and physically approximates well ISA temperature lapse rates. Fractional mass scale-heights have been calculated for both ISAOM and NLPAM and compared to ISA values. The agreement is especially good between ISA and NLPAM, as was expected. The ISOAM can also be extended into lower heterosphere for approximate pressure and density calculations. The parabolic vertical nonlinear temperature distribution can be extended to higher-order polynomials describing also mesospheric temperature profiles

Improving Airplane Touchdown Control by Utilizing the Adverse Elevator Effect

The main objective of this original research article is to understand the short-term dynamic behavior of the transport-category airplane during landing flare elevator control application. Increasing the pitch angle to arrest the sink rate, the elevator will have to produce negative lift to rotate the airplane’s nose upward. This has an immediate adverse effect of initially accelerating airplane downward. A mathematical model of landing flare based on the flat-Earth longitudinal dynamics of rigid airplane was developed which is realistic only on very short time-scales as pitch stiffness and damping were neglected. Pilot control scenarios using impulse and step elevator pull-up and push-over were used. Laplace integral transforms were used to transform ordinary differential equations into algebraic ones in complex domain. Transfer functions were defined for airplane response in pitch, angle of attack (AOA) and height. Based on the understanding and utilization of the adverse elevator effect a new landing flare technique is suggested which can substantially reduce scatter of touchdown points and increase consistency of landings. The new pull-push landing touchdown technique could reduce the probability of runway overruns and increase airframe life-time and is especially useful when landing on contaminated runways and/or during Land and Hold Short (LAHSO) operations