Thus we obtain simulaneous equations: The landing is smooth. There is no wind speed on the ground. The data sets are below: The surface of the runway is uniform. However later predicted data falls well out of range with the actual velocities, seen in the table: If the plane were to be turning while landing, it would increase the friction of the tires and we would need to consider the force needed to change the direction component of its velocity.
The aeroplane acts as a point. When it has slowed down enough this is augmented by a constant force from the wheel brakes. This simplifies the complex aerodynamics and drag by suggesting that we can consider the plane as a single point at its centre of mass rather than as a whole body.
Case 1 Plane initially lands, with only air resistance providing deceleration force. If we consider it to occupy space in three dimensions, this alters our original drag equation, as now air resistance acts at a cross- sectional area, A, of the plane, rather than a single point.
The runway is completely level. So now in time, t, the plane covers a distance: The task has already provided us with data for the velocity each second from 0 to 26 to aid with the modelling cycle, which will be discussed later in order to test our models.
The first case is before the braking force is applied; the second model adds this force. The landing is completely straight. However in 26 seconds, the fuel burnt will be a tiny proportion of its ,kg mass. Our two final equations are: An aeroplane of mass ,kg comes in to land at a runway.
This would mean that the mass of the plane decreased, hence its inertia and resistance to deceleration decreased. The aerodynamics of the plane do not change. The weather conditions do not change. The fuel burnt during landing is negligible. From the data given see section 4we know the motion is split into before and after the brakes are applied.
This is the most signficant since it has a direct consequence for the air resistance experienced by the plane. After touchdown it initially slows down from air resistance. We can relax assumption 2, that the plane acts as a single point in space. That is, the plane does not deploy any flaps, ailerons or elevators during landing.KS5 Mathematics and Further Maths Overview At AS and A2 level, all students follow a common course in Core Mathematics with additional modules in either Mechanics or Statistics, leading to accreditation by OCR (MEI).
Di↵erential Equations Coursework - ‘Aeroplane Landing’killarney10mile.com March 14th, Contents 1 Introduction 2 Sample coursework for Differential Equations (DE) "Modelling an Aeroplane" for OCR MEI A-level Maths.5/5(1).
Apr 27, · differential equations mei coursework watch. Announcements. Could these business ideas really work? Vote now and have your say. OCR MEI Differential Equations (DE), Tuesday 9th June ; Differential Equations help (MEI) MEI Mathematics C3 Coursework ; see more. Related university courses.
Sample coursework for Differential Equations (DE) "Modelling an Aeroplane" for OCR MEI A-level Maths. Original at killarney10mile.com MEI Differential Equations.
OCR Advanced GCE Unit Assessment Sheet A: Work Based on the Modelling Cycle ; Coursework must be available for moderation by OCR. GCW RevisedSeptember CAS/A Oxford Cambridge and RSA Examinations. MEI Differential Equations. OCR Advanced GCE Unit Assessment Sheet B Candidates will model a real-life situation of their own choice which requires the use of differential equations.
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