{ "cells": [ { "cell_type": "markdown", "id": "a5a73515", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Forward Flight" ] }, { "cell_type": "markdown", "id": "449c23a3", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "```{epigraph}\n", "\"The problem of the rotor in steady forward flight is the problem of defining the magnitude and direction of airflow encountered by each blade element\"\n", "\n", "-- Alfred Gessow (Aerodynamics of the Helicopter) \n", "```" ] }, { "cell_type": "markdown", "id": "97225998", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "Discussing about the details of forward flight state aerodynamics is also the perfect time to talk about the 2D aerodynamic characteristics of the airfoil sections that make up the blades of the rotor. You would not be prepostrously wrong in assuming that if the blade sections are made up of an airfoil with better airfoil characteristics then the overall rotor efficiency would be improved. 'Efficiency' of the rotor here refers to just the profile + induced power consumption of the rotor but in literature this term can also be used to refer to the acoustic noise or vibratory characteristics of the rotor. These are not within the scope of this course so we'll just end up focussing on rotor power consumption. But what does 'better airfoil characteristics' precisely mean? Is it just larger $C_l/C_d$? Larger stall angle of attack? The way the question has been posed might suggest that indeed there is something *extra* that needs to be accounted for or considered in order to improve rotor performance in forward flight. What that '*extra*' might be would become clear as the various aerodynamic phenomena, encountered by the rotor, in forward helicopter flight are discussed. " ] }, { "cell_type": "markdown", "id": "676c91de", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "On a conventional helicopter, the rotor is the sole entity responsible for generating thrust to counter the weight as well as the fuselage drag. While this characteristic itself leads to interesting aerodynamics and rotor performance attributes, there are a ton of pecularities arising just from edgewise rotor flight." ] }, { "cell_type": "markdown", "id": "ef0ed79b", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "
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UH-60A Helicopter [source]

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" ] }, { "cell_type": "markdown", "id": "150ee71d", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Fixed-wing wake vs Rotary-wing wake" ] }, { "cell_type": "markdown", "id": "9e21747f", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "
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Wing tip vortices behind a Boeing C-17 Globemaster [source]\n", "

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Wing tip vortices behind a McDonnell Douglas F/A-18 Hornet [source]\n", "

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" ] }, { "cell_type": "markdown", "id": "32d9959d", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ " \n", "\n", "
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Rotor tip vortex trajectories at difference advance ratios [source]

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\n", "\n", " \n", "\n", "- Note the changing wake pattern with $\\mu$\n", "- $v_i$ due to vortex-induced velocity \n", " - Biot-Savart law\n", "- high $v_i$ with tightly spaced rings in hover\n", " - high induced power\n", "- low $v_i$ when rotor quickly moves away \n", " - low *induced* power\n", " - fast forward flight \n", " - rotor in climb \n", "- vortex-based methods for better accuracy\n", " - free-wake\n", " - CFD\n", " " ] }, { "cell_type": "markdown", "id": "d60e0a34", "metadata": { "cell_style": "center", "slideshow": { "slide_type": "subslide" } }, "source": [ " \n", "\n", "
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Free-wake simulation of a 4 bladed rotor in forward flight

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" ] }, { "cell_type": "code", "execution_count": 6, "id": "aea9c71e", "metadata": { "cell_style": "center", "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/jpeg": 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\n", "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import YouTubeVideo\n", "YouTubeVideo('7PcowKB_Dwc', start=0, end=40, width=750, height=400)" ] }, { "cell_type": "markdown", "id": "9d1dfb41", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Induced power" ] }, { "cell_type": "markdown", "id": "c520e70e", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "The induced velocity in forward flight is stated below. It is to be assumed as agiven. It can be derived using the same principles that the expression for hover and climb cases were obtained, and is again based on the uniform inflow velocity assumption. " ] }, { "cell_type": "markdown", "id": "cf342739", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "
\n", " \n", "

Net inflow

\n", "
\n", "\n", "$$v_i = \\frac{T}{2\\rho A U}$$" ] }, { "cell_type": "markdown", "id": "78ae4ec5", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "where $U = \\left | \\bar{V_{\\infty}} + \\bar{v_i} \\right |$ is the vector sum of the oncoming flow velocity and the induced flow velocity. This result is consistent with the expressions obtained for hover and axial flight in that it reduces to the corresponding expressions when appropriate substitutions are made for $U$ and this is shown below. The induced power is then simply given by $P_i=Tv_i$. Note that $\\alpha$ in the proceeding results refers to the shaft tilt angle from the vertical position (and not angle of attack) which by convention is taken as positive for a rearward rotor disk tilt." ] }, { "cell_type": "markdown", "id": "174dfbf4", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Hover" ] }, { "cell_type": "markdown", "id": "5b7165c3", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "
\n", " \n", "

Hover

\n", "
\n", "\n", "\\begin{equation}\n", "\\begin{aligned}\n", "v_{i} &=\\frac{T}{2 \\rho A U} \\\\\n", "&=\\frac{T}{2 \\rho A \\sqrt{\\left(V_{\\infty} \\cos \\alpha\\right)^{2}+\\left(-V_{\\infty} \\sin \\alpha+v_{i}\\right)^{2}}} \\\\\n", "&=\\frac{T}{2 \\rho A \\sqrt{V_{\\infty}^{2} \\cos ^{2} \\alpha+V_{\\infty}^{2} \\sin ^{2} \\alpha-2 V_{\\infty} \\sin \\alpha v_{i}+v_{i}^{2}}} \\\\\n", "&=\\frac{T}{2 \\rho A \\sqrt{V_{\\infty}^{2}-2 V_{\\infty} \\sin \\alpha v_{i}+v_{i}^{2}}} \\\\\n", "&=\\frac{T}{2 \\rho A \\sqrt{v_{i}^{2}}} \\\\\n", "&=\\frac{T}{2 \\rho A v_{i}} \\\\\n", "v_{i}^{2} &=\\frac{T}{2 \\rho A} \\\\\n", "v_{i} &=\\sqrt{\\frac{T}{2 \\rho A}}\n", "\\end{aligned}\n", "\\end{equation}" ] }, { "cell_type": "markdown", "id": "00c8106c", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Vertical climb" ] }, { "cell_type": "markdown", "id": "1bb5813c", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "
\n", " \n", "

Vertical climb

\n", "
\n", "\n", "\\begin{equation}\n", "\\begin{aligned}\n", "v_{i} &=\\frac{T}{2 \\rho A \\sqrt{V_{\\infty}^{2}-2 V_{\\infty} \\sin \\alpha v_{i}+v_{i}^{2}}} \\\\\n", "&=\\frac{T}{2 \\rho A \\sqrt{V_{\\infty}^{2}+2 V_{\\infty} v_{i}+v_{i}^{2}}} \\\\\n", "&=\\frac{T}{2 \\rho A\\left(V_{\\infty}+v_{i}\\right)} \\\\\n", "&=-\\frac{V_{\\infty}}{2}+\\sqrt{\\frac{T}{2 \\rho A}+\\frac{V_{\\infty}^{2}}{4}} \\\\\n", "&=-\\frac{V_{\\infty}}{2}+\\sqrt{v_{h}^{2}+\\frac{V_{\\infty}^{2}}{4}}\n", "\\end{aligned}\n", "\\end{equation}" ] }, { "cell_type": "markdown", "id": "6a144c5f", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Low forward speed " ] }, { "cell_type": "markdown", "id": "6c75bed6", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "
\n", " \n", "

Low speed forward flight

\n", "
\n", "\n", "\\begin{equation}\n", "\\begin{aligned}\n", "v_{i} &=\\frac{T}{2 \\rho A \\sqrt{V_{\\infty}^{2}-2 V_{\\infty} \\sin \\alpha v_{i}+v_{i}^{2}}} \\\\\n", "& \\approx \\frac{T}{2 \\rho A \\sqrt{V_{\\infty}^{2}+v_{i}^{2}}} \\\\\n", "\\Rightarrow v_i &=\\sqrt{-\\frac{V_{\\infty}^{2}}{2}+\\sqrt{\\left(\\frac{T}{2 \\rho A}\\right)^{2}+\\frac{V_{\\infty}^{4}}{4}}} \\\\\n", "&=\\sqrt{-\\frac{V_{\\infty}^{2}}{2}+\\sqrt{v_{h}^{4}+\\frac{V_{\\infty}^{4}}{4}}}\n", "\\end{aligned}\n", "\\end{equation}" ] }, { "cell_type": "markdown", "id": "c2b57c24", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "The low forward speed assumption of $\\alpha\\approx 0$ is generally valid for advance ratios $\\mu<0.15$, where $\\mu = \\frac{V_{\\infty}}{\\Omega R}$." ] }, { "cell_type": "markdown", "id": "d3ab0160", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## High forward speed" ] }, { "cell_type": "markdown", "id": "5e2a9c47", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "
\n", " \n", "

High speed forward flight

\n", "
\n", "\n", " \n", " \n", " \n", "\n", "\\begin{equation}\n", "\\begin{aligned}\n", "v_{i} &=\\frac{T}{2 \\rho A \\sqrt{V_{\\infty}^{2}-2 V_{\\infty} \\sin \\alpha v_{i}+v_{i}^{2}}} \\\\\n", "& \\approx \\frac{T}{2 \\rho A \\sqrt{V_{\\infty}^{2}}} \\\\\n", "&=\\frac{T}{2 \\rho A V_{\\infty}}\n", "\\end{aligned}\n", "\\end{equation}" ] }, { "cell_type": "markdown", "id": "8782c12a", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "The inflow variation with forward speed can then be obtained by *stitching-up* the results in the different domains. Once the induced velocity is known, the induced power can be simply obtained as $Tv_i$. As was mentioned earlier for hover, large mass flow through the rotor disk is key to thrust efficiency of a rotor. When a rotor is tilted for forward flight, a component of the oncoming flow velocity goes through the rotor disk. This increases the effective mass flow rate of air through the disk much like in the rotor climb scenario. Consequently, a smaller increase in velocity needs to be imparted to the flow to get the required momentum change and leads to the reduction in $v_i$ obtained." ] }, { "cell_type": "markdown", "id": "63123cda", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "
\n", " \n", "

Rotor inflow versus forward flight speed

\n", "
" ] }, { "cell_type": "markdown", "id": "90838da4", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Descent flight" ] }, { "cell_type": "markdown", "id": "7c1de4b7", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "Descent flight in rotorcraft is usually undertaken at very low speeds. Fast descent speeds can lead to large flow recirculation and turbulence in the flow, leading to high vibrations and loss of control. There are three distinct states that exist with increasing descent flight velocities of a rotor - " ] }, { "cell_type": "markdown", "id": "a8f897bc", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "Vortex ring state \n", "- $V<0$ but $V+v_i>0$" ] }, { "cell_type": "markdown", "id": "c31451f0", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "Turbulent wake state\n", "- $V<0$ and $V+v_i<0$, but $V+2v_i>0$" ] }, { "cell_type": "markdown", "id": "ddff2c56", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "Windmill brake state\n", "- $V<0$, $V+v_i<0$, $V+2v_i<0$" ] }, { "cell_type": "markdown", "id": "3f5cddb1", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "
\n", " \n", "

Rotor descent flight states [source]

\n", "
" ] }, { "cell_type": "code", "execution_count": 7, "id": "d4878d84", "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/jpeg": 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"text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import YouTubeVideo\n", "YouTubeVideo('HjeRSDsy-nE', width=750, height=400,start=133)" ] }, { "cell_type": "code", "execution_count": 8, "id": "50336282", "metadata": { "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "image/jpeg": 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\n", "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import YouTubeVideo\n", "YouTubeVideo('05_WFvh9ISk', width=750, height=400)" ] }, { "cell_type": "markdown", "id": "7215a3ef", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "The following show induced velocity of the rotor as a function of climb velocity (negative climb velocity denotes a descent flight state). While not explicitly derived as part of the lectures, the inflow velocity during the windmill brake state, i.e. when the rotor acts as a wind turbine, can be derived using momentum theory along the lines of the derivation for the normal working state. The variation would then be as denoted by the solid lines. However, if the results were simply extended (denoted using dashed lines) to regions that we now understand to be the turbulent wake state or the vortex ring state, the results would not match with that observed in reality (solid lines). This is because the flow is highly turbulent in these scenarios and the simple momentum theory does not capture that and incurs an error. An alternate way of presenting the same results is by plotting the total inflow velocity on the y-axis. When experimental measurements are laid on this figure, notwithstanding the scatter in the measurements, they largely follow the trend of the solid lines. \n", "\n", "**It is worth noting that these experimental results are not based on a measured induced velocity in wind tunnel or free-flight, rather the total power consumption of the rotor was measured and simple momentum theory-like relations were assumed to arrive at the corresponding uniform induced inflow velocity. This is why the second plot of total inflow versus climb velocity is used because the total power measured in experiments can be directly used to obtain the net inflow since climb power and induced power cannot be separately measured. Another feature apparent from the figures is that momentum theory, as simple as it is, is capable of predicting the average rotor power consumption very well.** \n", "\n", "*Note that convention followed within these figures is such that $v$ is used to represent inflow velocity $v_i$, $V$ is used to denote climb velocity $V_c$, and $v_h$ refers to the induced velocity at hover.*" ] }, { "cell_type": "markdown", "id": "6de8c7f7", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "
\n", " \n", " \n", " \n", "
\n", "\n", "
\n", "

Rotor induced velocity during axial flight states [source]

\n", "

Net rotor inflow during axial flight states [source]

\n", "

Inflow results based on experimental measurement of different rotors [source]

\n", "
\n" ] }, { "cell_type": "markdown", "id": "1cdf11ae", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "(content:5_FF_T_La:labels)=\n", "## Rotor aerodynamics assymetry" ] }, { "cell_type": "markdown", "id": "3061eded", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "As soon as a rotor starts moving edgewise, a lateral assymetry is introduced with regard to the total in-plane velocity. This assymetry is most prominent at the azimuth locations $\\psi=90°$ and $\\psi=270°$ and decreases progressively to no assymetry at azimuth locations $\\psi=0°$ and $\\psi=180°$." ] }, { "cell_type": "markdown", "id": "f891ca15", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "
\n", " \n", "

Tangential velocity distribution in hover versus forward flight (at $\\psi$ =90°)

\n", "
" ] }, { "cell_type": "markdown", "id": "b0ebaffb", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Reverse flow" ] }, { "cell_type": "markdown", "id": "8dcfc564", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "Along with the in-plane flow assymetry in the lateral direction, a reverse flow region occurs in forward flight. This is of concern because the blade sections within this region effectively have an angle of attack close to 180° and are no longer aerodynamically efficient. There is no minimum threshold speed for the reverse flow region to occur but it is not of major concern for low speed flight since rotors generally have a root cutout region of about 20%. Based on the equations given below, this means that only for $\\mu > 0.2$ do blade airfoil sections start experiencing reverse flow." ] }, { "cell_type": "markdown", "id": "3f664dec", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "
\n", " \n", "

Reverse flow region during forward flight

\n", "
" ] }, { "cell_type": "markdown", "id": "435a9011", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "\n", "$$ V_{T}=\\Omega \\cdot y+V_{F} \\cdot \\sin \\Psi $$\n" ] }, { "cell_type": "markdown", "id": "41fce956", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "$$ V_{T}=\\Omega \\cdot y+V_{F} \\cdot \\sin \\Psi=0 $$\n" ] }, { "cell_type": "markdown", "id": "e670b9ff", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "$$ y=\\frac{-V_{F} \\cdot \\sin \\Psi}{\\Omega}=-\\frac{V_{F}}{\\Omega R} \\sin \\Psi \\cdot R=-\\mu \\cdot \\sin \\Psi \\cdot R$$" ] }, { "cell_type": "markdown", "id": "a749f728", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Profile power" ] }, { "cell_type": "markdown", "id": "8c502a02", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "The drag due to fluid viscosity and due to pressure distribution over the airfoil surface manifests itself within the airfoil drag coefficient. The power required by the rotor to overcome these drag forces can be evaluated by integrating the power required to overcome drag at each blade section and averaged over the azimuth. " ] }, { "cell_type": "markdown", "id": "2cfc8ae6", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "
\n", " \n", " \n", "
\n", "\n", "
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Blade section drag due to in-plane velocity

\n", "

Rotor in forward flight

\n", "
\n" ] }, { "cell_type": "markdown", "id": "b732fca3", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "\n", "\\begin{equation}\n", "\\begin{array}{l}\n", "\\displaystyle P_{0}=\\frac{N_{b}}{2 \\pi} \\int_{0}^{2 \\pi } \\int_{0}^{R} P_{0}^{\\prime} d y d \\Psi \\\\\n", "\\displaystyle P_{0}=\\frac{N_{b}}{2 \\pi} \\int_{0}^{2 \\pi } \\int_{0}^{R} D^{\\prime}.V_T d y d \\Psi \\\\\n", "\\displaystyle P_{0}=\\frac{N_{b}}{2 \\pi} \\int_{0}^{2 \\pi } \\int_{0}^{R} \\frac{1}{2} \\rho C_{d 0} c V_{T}^{2} \\cdot\\left|V_{T}\\right| d y d \\Psi \\\\\n", "\\displaystyle P_{0}=\\frac{N_{b}}{4 \\pi} \\rho C_{d 0} c \\int_{0}^{2 \\pi} \\int_{0}^{R} V_{T}^{2} \\cdot\\left|V_{T}\\right| d y d \\Psi \\\\\n", "\\displaystyle P_{0}=\\frac{N_{b}}{4 \\pi} \\rho C_{d 0} c \\cdot\\left(\\int_{0}^{2 \\pi} \\int_{0}^{R} V_{T}^{3} d y d \\Psi-2 \\cdot \\int_{\\pi}^{2 \\pi} \\int_{0}^{\\frac{-V_{F}sin\\Psi}{\\Omega}} V_{T}^{3} d y d \\Psi\\right) \\\\\n", "\\displaystyle P_{0}=\\frac{N_{b}}{4 \\pi} \\rho C_{d 0} c\\left(\\int_{0}^{2 \\pi} \\int_{0}^{R}\\left(\\Omega \\cdot y+V_{F} \\cdot \\sin \\Psi\\right)^{3} d y d \\Psi-2 \\cdot \\int_{\\pi}^{2 \\pi} \\int_{0}^{\\frac{-V_{F} \\cdot \\sin \\Psi}{\\Omega}} \\left(\\Omega \\cdot y+V_{F} \\cdot \\sin \\Psi\\right)^{3} d y d \\Psi\\right) \\\\\n", "\\displaystyle P_{0}=\\frac{N_{b}}{4 \\pi} \\rho C_{d 0} c\\left(\\frac{\\pi}{2} \\Omega^{3} R^{4}+\\frac{3 \\pi}{2} \\Omega R^{2} V_{F}^{2}+2 \\cdot \\frac{3 \\pi V_{F}^{4}}{32 \\Omega}\\right) \\\\\n", "\\displaystyle P_{0}=\\frac{N_{b}}{4 \\pi} \\rho C_{d 0} c\\left(\\frac{\\pi}{2} \\Omega^{3} R^{4}+\\frac{3 \\pi}{2} \\Omega R^{2} V_{F}^{2}+\\frac{3 \\pi V_{F}^{4}}{16 \\Omega}\\right) \\\\\n", "\\displaystyle P_{0}=\\frac{N_{b}}{8} \\rho C_{d 0} c \\Omega^{3} R^{4}\\left(1+3 \\frac{V_{F}^{2}}{\\Omega^{2} R^{2}}+\\frac{3 V_{F}^{4}}{8 \\Omega^{4} R^{4}}\\right) \\\\\n", "\\displaystyle P_{0}=\\frac{1}{8} \\rho \\sigma A C_{d 0} V_{TIP}^{3}\\left(1+3 \\mu^{2}+\\frac{3}{8} \\mu^{4}\\right)\\\\\n", "\\end{array}\n", "\\end{equation}" ] }, { "cell_type": "markdown", "id": "9a9c7ef5", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Parasite power" ] }, { "cell_type": "markdown", "id": "f5c25f02", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "The power expended in order to overcome the fuselage drag of a helicopter is refered to as the parasite power. It is simply the parasite drag times the forward speed where the parasite drag itself is usually stated as an equivalent flat plate area $f$. Since fuselage attitude largely remains the same at any speed, $f$ can be assumed a constant." ] }, { "cell_type": "markdown", "id": "576ccaa7", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "$$P_p = D_p*V_{\\infty} = \\frac{1}{2}\\rho V_f^3 f$$" ] }, { "cell_type": "markdown", "id": "b29ea3e9", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Power bucket curve" ] }, { "cell_type": "markdown", "id": "074f4a1c", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "The consumed power breakdown of the entire helicopter is shown below. The power required by the tail rotor $P_{TR}$ which can be fairly approximated as a fixed percentage (about 10%) of the total power required by the main rotor [^TailRotor]. $P_a$ here refers to accesories power for onboard equipment and $P_{tl}$ refers to additional power required to overcome transmission losses. These three power components are small in comparision of the main rotor power $P_i+P_0$ and the helicopter parasite power $P_p$. The characteristic 'bucket' curve is a byproduct of the interplay between the latter 3 power components.\n", "\n", "[^TailRotor]: Alternately, the tail rotor power can be also obtained from first principles using BET or momentum theory. " ] }, { "cell_type": "markdown", "id": "c63dbc49", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "
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Total helicopter power consumption versus forward speed

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