{ "cells": [ { "cell_type": "markdown", "id": "eb31da34", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Performance: Aérospatiale SA 315B Lama" ] }, { "cell_type": "markdown", "id": "1c80da7e", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "The Aérospatiale SA 315B Lama was known for its superior high altitude performance and was the go-to helicopter for high-altitude operations in all the high-altitude mountain ranges in the world. The requirements of high altitude operation are relatively simple and can be inferred from the basic physics encountered within the scope of the momentum theory and blade element theory. Operating a helicopter in hover mode in high altitudes implies that the induced velocity would be high, which implies a correspondingly large power requirement. So it is apparent that the installed engines would need to have a high power rating. However, just increasing the installed engine power is not a sure shot solution since the rotor blades stall needs to be avoided before peak operational altitude is achieved. Recall the expression derived using BET- " ] }, { "cell_type": "markdown", "id": "f97668e4", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "
\n", " \n", "

Aérospatiale SA 315B Lama [source]

\n", "
" ] }, { "cell_type": "markdown", "id": "35d3e595", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "$$ d C_{T} =\\frac{\\sigma}{2} C_{l_{\\alpha}} (\\theta-\\phi) r^{2} d r$$" ] }, { "cell_type": "markdown", "id": "f2f6a586", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "In order to fly at high altitudes, the rotor needs to operate at a higher $C_T$ for the same MTOW. This is because $C_T$ is a function of the atmospheric density. Clearly, the quantity on the RHS in the equation above needs to increase with altitude - $\\theta$ being the only variable that can be directly influenced. Beyond a certain $\\theta$ the blades stall and no further increase in $\\theta$ leads to an increase in rotor thrust. Consequently, for high altitude performance the rotor needs to be designed such that there is large margin between the required pitch angles of the blade required to hover at sea level and the maximum pitch angle before the blade stalls. This can be achieved by a judicious choice of the airfoil (higher $C_{l_{\\alpha}}$), or increasing the number of rotor blades or increasing the chord of the blades (higher $\\sigma$)." ] }, { "cell_type": "markdown", "id": "38354370", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "Large mass flow through the rotor disk is key to hover efficiency of rotorcraft. A single powerful turboshaft engine, skids instead of wheels, a skeletal tail boom etc all minimised structural weight in case of the Lama. The high engine rating of 649 kW (de-rated to 410 kW) ensured that the helicopter had a substantial power margin - at 1500 kg of take-off weight and rotor diameter of 11 m, momentum theory calculations show that only about 116 kW of power is needed to maintain hover at sea-level." ] }, { "cell_type": "code", "execution_count": 1, "id": "6a60510b", "metadata": { "hide_input": true, "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "image/jpeg": 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