Download descent calculator

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Descent Calculator Used to calculate where the pilot should start their descent in flight simulators Click link to download: Descent Calculator Continuous Residence and Get Airplane Descent Calculator PR old version APK for Android. Download. About Airplane Descent Calculator PR. Calculate distance or rate of descent to get target

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IntroductionIn the realm of optimization problems, the steepest descent method serves as a fundamental tool for finding the minimum value of a function. This article introduces a steepest descent calculator, equipped with an efficient algorithm to facilitate numerical computations.How to UseTo utilize the steepest descent calculator, follow these simple steps:Input the initial guess for the minimum value.Define the function to be optimized.Specify the tolerance level for convergence.Click the “Calculate” button to initiate the computation.FormulaThe steepest descent method, also known as the gradient descent method, iteratively updates the current guess by moving in the direction of the negative gradient of the function. The formula for updating the guess x at each iteration k is given by:Where:xk​ is the current guess.α is the step size, also known as the learning rate.∇f(xk​) represents the gradient of the function at point xk​.Example SolveIteration 1:FAQ’sQ: What is the steepest descent method?A: The steepest descent method is an iterative optimization technique used to find the minimum value of a function by moving in the direction of the negative gradient.Q: How does the steepest descent calculator work?A: The steepest descent calculator implements the steepest descent algorithm, allowing users to input initial values and function definitions to find the minimum of a given function.Q: What is the significance of the learning rate in the steepest descent method?A: The learning rate determines the step size taken in the direction of the negative gradient. It influences the convergence rate and stability of the algorithm.ConclusionThe steepest descent calculator presented here offers a convenient means of performing optimization tasks efficiently. By leveraging the steepest descent method, users can find the minimum value of a function with ease.

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US4346288A - Fuel saving aircraft descent calculator - Google Patents Fuel saving aircraft descent calculator Download PDF Info Publication number US4346288A US4346288A US06/202,601 US20260180A US4346288A US 4346288 A US4346288 A US 4346288A US 20260180 A US20260180 A US 20260180A US 4346288 A US4346288 A US 4346288A Authority US United States Prior art keywords altitude distance scale descent calculator Prior art date 1980-10-31 Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.) Expired - Lifetime Application number US06/202,601 Inventor Edward T. Foster Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.) Individual Original Assignee Individual Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.) 1980-10-31 Filing date 1980-10-31 Publication date 1982-08-24 1980-10-31 Application filed by Individual filed Critical Individual 1980-10-31 Priority to US06/202,601 priority Critical patent/US4346288A/en 1982-08-24 Application granted granted Critical 1982-08-24 Publication of US4346288A publication Critical patent/US4346288A/en 2000-10-31 Anticipated expiration legal-status Critical Status Expired - Lifetime legal-status Critical Current Links USPTO USPTO PatentCenter USPTO Assignment Espacenet Global Dossier Discuss Images Classifications G—PHYSICS G06—COMPUTING; CALCULATING OR COUNTING G06G—ANALOGUE COMPUTERS G06G1/00—Hand manipulated computing devices G06G1/0005—Hand manipulated computing devices characterised by a specific application G06G1/0063—Hand manipulated computing devices characterised by a specific application for calculating fuel consumption Definitions This invention relates to aircraft navigation equipment, and more particularly to a manually operable descent calculator for determining the optimal fuel efficient point at which to commence a descent. U.S. Pat. No. 4,011,987 issued Mar. 15, 1977 to

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Displayed. the figures in the 110- and 120,000 pound columns are assigned negative values, since a lower gross aircraft weight will permit a closer approach before beginning a descent, while the figures under the 140- and 150,000 pound columns are assigned positive values. Each of the columns extends from the top towards the bottom of the altitude scale, and progressively decrease in value towards the bottom of the scale in correspondence with the decreasing effect of weight on descent distance at the lower altitudes. the weight correction factor is determined in a manner similar to the wind correction factor by merely locating the correction factor in the column corresponding to the actual aircraft weight adjacent the aircraft's altitude. An overall correction factor is determined by merely aggregating the wind and weight correction factors. For example, assuming an aircraft with a gross weight of 110,000 pounds is flying with a 20 knot tailwind at an altitude of 35,000 feet, the weight correction factor would be minus 6, while the wind correction factor would be plus 2.5, for a net correction factor of minus 3.5. A more precise distance for commencing a descent, and corresponding greater fuel savings, is calculated by subtracting 3.5 from the mileage otherwise indicated by the calculator for beginning the descent. the calculator is also very useful in monitoring the aircraft's adherence to a fuel efficient descent profile once the descent had begun. the pilot keeps stick 16 in place with the target altitude aligned with the target distance, and reads the calculated distance corresponding to any given altitude during the descent. This calculated distance is corrected by a net wind and weight correction factor for the particular altitude, to tell the pilot whether he is at the correct distance for the given altitude. the calculator is particularly. Descent Calculator Used to calculate where the pilot should start their descent in flight simulators Click link to download: Descent Calculator Continuous Residence and

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To provide a descent rate, which is a more difficult procedure than an idle descent. an aircraft descent calculator which is capable of taking into account and adjusting to different conditions or aircraft weight, wind, aircraft speed and altitude, and without unduly complicating the device. Another object of the invention is the provision of a novel and improved aircraft descent calculator which provides a fuel effecient descent profile including changes in aircraft speed during the descent. a manually operable calculator for optimizing aircraft fuel consumption during descent from an actual altitude and distance to a target altitude and distance is provided with a first member having a distance scale displayed thereon, and at least one additional member having an altitude scale displayed thereon. the first and additional members are mutually secured and alignable, and their respective distance and altitude scales are proportioned such that, when a target distance on the distance scale is aligned with a target altitude on the altitude scale, the actual altitude on the altitude scale is aligned with a desired fuel efficient distance for commencing the descent, for a given aircraft weight and speed and a given wind condition. an aircraft weight and wind correction scale is provided, by which a correction factor can be obtained to correct the indicated distance for commencing the descent. the correction scale preferrably comprises a first portion for determining a gross correction factor corresponding to a maximum altitude, and a second scale portion which proportions the gross correction factor in accordance with the actual aircraft altitude. a plurality of altitude scales are provided on a corresponding plurality of members which are secured for relative aligned movement with the distance scale member. Each altitude scale is proportioned to correspond with a respective aircraft speed, thereby enabling the calculator to give accurate

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Altitude scales being respectively proportioned so that, when a target distance on the distance scale is aligned with a target altitude on a respective altitude scale, the actual altitude on said respective altitude scale is aligned with a desired fuel efficient distance on the distance scale for commencing the descent, and means mutually securing said first member and said display means for relative aligned movement. 13. The calculator of claim 12, said display means comprising a plurality of members, each of said members having a respective altitude scale displayed thereon, and secured for relative aligned movement with respect to said first member. 14. The calculator of claim 7 or 12, further comprising an aircraft weight and wind correction scale means, said correction scale means providing a correction factor to adjust the indicated distance for commencing a descent based upon the aircraft weight and prevailing wind conditions. US06/202,601 1980-10-31 1980-10-31 Fuel saving aircraft descent calculator Expired - Lifetime US4346288A (en) Priority Applications (1) Application Number Priority Date Filing Date Title US06/202,601 US4346288A (en) 1980-10-31 1980-10-31 Fuel saving aircraft descent calculator Applications Claiming Priority (1) Application Number Priority Date Filing Date Title US06/202,601 US4346288A (en) 1980-10-31 1980-10-31 Fuel saving aircraft descent calculator Publications (1) Publication Number Publication Date US4346288A true US4346288A (en) 1982-08-24 Family ID=22750546 Family Applications (1) Application Number Title Priority Date Filing Date US06/202,601 Expired - Lifetime US4346288A (en) 1980-10-31 1980-10-31 Fuel saving aircraft descent calculator Country Status (1) Country Link US (1) US4346288A (en) Cited By (16) * Cited by examiner, † Cited by third party Publication number Priority date Publication date Assignee Title US4564750A (en) * 1983-07-07 1986-01-14 Olsen Pal B Device for combination of data US4580814A (en) * 1984-04-09 1986-04-08 Berler Robert M Weather guide for deriving typical weather conditions US5148006A (en) * 1989-10-30 1992-09-15 Minnesota Mining

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Accuracy the correction factors on one side of the calculator can differ from those on the other side in accordance with their respective speeds. Thus, the calculator can be "programmed" for four airspeeds simultaneously. This can be very helpful and result in considerable fuel savings under present Air Traffic Control conditions in which the pilot may be required to change air speeds, often several times, during a descent. This is potentially very wasteful of fuel, but use of the calculator enables fuel consumption to be minimized. Because the pilot is given optimum air speed/altitude/distance information at any point on the descent profile for four different air speeds, the transition to a different air speed/altitude/distance profile can be made economically. For example, for an aircraft on a 280 knot descent profile, a sudden request to speed up to 320 knots might cause the pilot to lower the nose to gain speed, with the result of the aircraft reaching lower altitude restrictions at an early point, and wasteful applications of power at the lower altitudes being required. If, on the other hand, the pilot has a calculator available and refers to the proper mileage/altitude for 320 knots, an orderly transition can be made to the 320 knot profile by an application of power to shallow the glide angle at a higher altitude, and then reducing power again to idle when the 320 knot profile is intercepted. By thus making the transition to a higher air speed descent at a higher altitude, a more fuel efficient total descent is achieved. In the opposite situation of initially descending at a higher air speed and being requested to slow to a lower air speed, the calculator again provides an orderly program to do so. The pilot would apply the speed brake to slow and steepen

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Profile to maximize fuel savings. Another object of the invention is the provision of a novel and improved aircraft descent calculator which provides a fuel effecient descent profile including changes in aircraft speed during the descent. In the accomplishment of these and other objects of the invention, a manually operable calculator for optimizing aircraft fuel consumption during descent from an actual altitude and distance to a target altitude and distance is provided with a first member having a distance scale displayed thereon, and at least one additional member having an altitude scale displayed thereon. The first and additional members are mutually secured and alignable, and their respective distance and altitude scales are proportioned such that, when a target distance on the distance scale is aligned with a target altitude on the altitude scale, the actual altitude on the altitude scale is aligned with a desired fuel efficient distance for commencing the descent, for a given aircraft weight and speed and a given wind condition. In addition, an aircraft weight and wind correction scale is provided, by which a correction factor can be obtained to correct the indicated distance for commencing the descent. The correction scale preferrably comprises a first portion for determining a gross correction factor corresponding to a maximum altitude, and a second scale portion which proportions the gross correction factor in accordance with the actual aircraft altitude. In the preferred embodiment, a plurality of altitude scales are provided on a corresponding plurality of members which are secured for relative aligned movement with the distance scale member. Each altitude scale is proportioned to correspond with a respective aircraft speed, thereby enabling the calculator to give accurate results for different descent speeds, and for descents involving decelerations or accelerations in speed. Additional calculator accuracy is achieved by proportioning the altitude. Descent Calculator Used to calculate where the pilot should start their descent in flight simulators Click link to download: Descent Calculator Continuous Residence and Get Airplane Descent Calculator PR old version APK for Android. Download. About Airplane Descent Calculator PR. Calculate distance or rate of descent to get target

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Savings, is calculated by subtracting 3.5 from the mileage otherwise indicated by the calculator for beginning the descent. The calculator is also very useful in monitoring the aircraft's adherence to a fuel efficient descent profile once the descent had begun. The pilot keeps stick 16 in place with the target altitude aligned with the target distance, and reads the calculated distance corresponding to any given altitude during the descent. This calculated distance is corrected by a net wind and weight correction factor for the particular altitude, to tell the pilot whether he is at the correct distance for the given altitude. The calculator is particularly useful for descents which involve a deceleration from one speed to a lower speed. The pilot would use the altitude and distance of the deceleration point as his first target, and use the calculator to determine the distance for beginning a high speed descent to that point along the distance corresponding to the higher speed. When that point is reached, the pilot can reset the calculator so that the ultimate target distance on the lower speed distance scale is aligned with the ultimate target altitude, and read the distance corresponding to the present altitude. A wind/weight correction factor would then be determined as described above. Extra distance necessary to decelerate can also be accounted for. In the example described above, assuming the aircraft was required to be slowed to 250 knots at 13,000 feet and 30 miles DME from an initial speed of 280 knots, and that a deceleration distance of two miles was required, the target altitude of 13,000 feet would be aligned with 32 miles on the 280 knot distance scale, rather than 30 miles. Referring now to FIGS. 4 and 5, a second embodiment of the invention is shown which offers several

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Altitude to be lost during the descent. 3. The calculator of claim 2, further comprising means having a second altitude scale displayed thereon, said second altitude scale being proportioned in terms of indicated air speed below a predetermined altitude, said first and second altitude scales being proportioned to correspond respectively to first and second aircraft speeds, said distance and second altitude scales being mutually alignable and proportioned so that, when a target distance on the distance scale is aligned with a target altitude on the second altitude scale, the actual altitude on the second altitude scale is aligned with a desired fuel efficient distance on the distance scale for commencing a descent to the target altitude and distance, for a given aircraft weight and speed and a given wind condition. 4. The calculator of claim 3, said second altitude scale being displayed on a third member which is mutually secured and alignable with said first member. 5. The calculator of claim 4, said correction scale being displayed on a fourth member which is mutually secured to said second and third members, said correction scale being alignable with either one of said first and second altitude scales. 6. The calculator of claim 1 or 2, said correction scale means including means for determining separate weight and wind correction factors, said separate correction factors being aggregable to a single correction factor. 7. A manually operable calculator for calculating a beginning of descent position to optimize aircraft fuel consumption during descent from an actual altitude and distance to a target altitude and distance, comprising:a first member having a distance scale displayed thereon, a plurality of additional members, each of said additional members being alignable with said first member, and having respective altitude scales displayed thereon extending over substantially equal altitude ranges, each of. Descent Calculator Used to calculate where the pilot should start their descent in flight simulators Click link to download: Descent Calculator Continuous Residence and

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Air Traffic Control conditions in which the pilot may be required to change air speeds, often several times, during a descent. This is potentially very wasteful of fuel, but use of the calculator enables fuel consumption to be minimized. the transition to a different air speed/altitude/distance profile can be made economically. For example, for an aircraft on a 280 knot descent profile, a sudden request to speed up to 320 knots might cause the pilot to lower the nose to gain speed, with the result of the aircraft reaching lower altitude restrictions at an early point, and wasteful applications of power at the lower altitudes being required. an orderly transition can be made to the 320 knot profile by an application of power to shallow the glide angle at a higher altitude, and then reducing power again to idle when the 320 knot profile is intercepted. the calculator again provides an orderly program to do so. The pilot would apply the speed brake to slow and steepen the angle of descent until the shallower low speed descent profile is intercepted, and then follow that profile. the present invention thus provides an accurate and easy to use tool for a pilot to determine and follow a fuel efficient descent profile. While numerous variations and modifications to the embodiments described above may occur to those skilled in the art, it is intended that the invention be limited only in terms of the appended claims. Landscapes Engineering & Computer Science (AREA) Theoretical Computer Science (AREA) Physics & Mathematics (AREA) Computer Hardware Design (AREA) General Physics & Mathematics (AREA) Traffic Control Systems (AREA) Abstract A manually operable calculator for optimizing aircraft fuel consumption during descent from an actual altitude to a target altitude/distance. Altitude and distance scales are provided which are alignable to determine