ATPL Performance - Class 6: Climbing.

Summary

In this educational aviation video, Grant explores the climb procedure, emphasizing the importance of understanding performance characteristics for safe flight. He explains how factors like angle of climb, rate of climb, and environmental influences affect aircraft performance. The video delves into the physics of flight, discussing the impact of mass, configuration, altitude, temperature, and engine failure on climb capabilities. Grant also clarifies the distinction between climb angle and flight path angle, and the significance of maintaining safe airspeeds and Mach numbers during ascent.

Takeaways

• 🛫 The climb phase of flight begins after takeoff and reaching screen height, and can also occur during the route or after a go-around.
• 📈 Climbing performance can be measured by either the angle of climb or the rate of climb, which are influenced by factors such as thrust, drag, and weight.
• 🔢 The angle of climb can be calculated using the equation involving lift, weight, thrust, and drag, with the sine of the angle representing the excess thrust over weight.
• 🏞 Environmental factors like altitude and temperature affect climb performance due to changes in air density and engine thrust output.
• ✈️ Aircraft configuration, such as the use of flaps and landing gear, increases drag and thus reduces the climb angle.
• 🚀 The climb gradient is maximized at a specific speed (VX) where the difference between thrust and drag is the greatest, differing between jet and propeller-driven aircraft.
• 🔄 Excess thrust is key to achieving a steeper climb angle, and anything that increases drag or reduces thrust will negatively impact climb performance.
• 🌡️ As altitude and temperature increase, air density decreases, leading to reduced engine thrust and a lower climb gradient.
• 💨 Wind does not affect the climb angle but influences the flight path angle, which is the aircraft's position relative to the ground.
• 📉 The rate of climb is maximized at a different speed (VY) where excess power is the greatest, and is influenced by similar factors as the angle of climb.
• 🚨 Flying at a constant indicated airspeed during climb results in increasing true airspeed and Mach number, necessitating a switch to climbing at a constant Mach number at a certain altitude to avoid exceeding speed limits.

Q & A

What is the main focus of the sixth class in the Performance Series presented by Grant?

The main focus of the sixth class is to understand the climb procedure in aviation, including the performance characteristics needed to achieve a safe and effective climb after takeoff.

What are the two primary factors that determine the steepness of an aircraft's climb?

The two primary factors that determine the steepness of an aircraft's climb are the angle of climb and the rate of climb.

How is the angle of climb in a steady climb calculated?

The angle of climb is calculated using the forces acting on the aircraft, where lift equals weight times cosine Theta and thrust equals drag plus weight times sine Theta. The sine of the angle (sine Theta) is equal to the excess thrust over weight.

What is the significance of the climb gradient in relation to the angle of climb?

The climb gradient is the vertical change over the horizontal change during the climb, and for small angles, it is roughly equal to the sine of the angle of climb, which helps in understanding how steep the climb is.

What is the term used to describe the speed that provides the best angle of climb, and what does it represent?

The term is 'VX', which represents the speed at which the aircraft achieves the best angle of climb, occurring where excess thrust is maximized.

How does aircraft configuration, such as flaps and landing gear, affect the climb performance?

Aircraft configuration that increases drag, such as flaps and landing gear, results in a lower excess thrust, leading to a smaller climb gradient and a less steep climb angle.

What is the difference between the climb angle and the flight path angle, and how does wind affect them?

The climb angle is the aircraft's position relative to the air mass, while the flight path angle is the aircraft's position relative to the ground. Wind does not affect the climb angle but does affect the flight path angle by altering the aircraft's horizontal movement over the ground.

What is the formula used to calculate the rate of climb, and what does it depend on?

The rate of climb is calculated using the formula 'Excess power over weight'. It depends on both the angle of climb and the true airspeed, as well as the excess power available.

What is the term 'VY' in aviation, and what does it signify?

VY is the term used to describe the speed for the best rate of climb. It signifies the speed at which the aircraft achieves the maximum rate of climb, occurring where excess power is maximized.

How does increasing altitude affect the aircraft's climb performance?

Increasing altitude affects the aircraft's climb performance negatively because it results in lower air density, which in turn reduces the thrust output of the engines, leading to less excess thrust and a smaller climb gradient.

What are the implications of climbing with a constant indicated airspeed, and how is this managed in practice?

Climbing with a constant indicated airspeed results in an increase in true airspeed and Mach number as altitude increases. To manage this and stay within safe speed ranges, pilots switch from climbing at a constant indicated airspeed to climbing at a constant Mach number at a specific changeover altitude.

Outlines

00:00

🛫 Understanding Climb Performance in Aviation

This paragraph introduces the topic of aircraft climb performance, explaining the factors that affect the steepness of the climb, such as environmental conditions and aircraft characteristics. It emphasizes the importance of understanding these factors for safe flight, especially in avoiding obstacles. The narrator, Grant, discusses the climb phase, which begins after takeoff and continues until the aircraft reaches its cruising altitude. The paragraph delves into the physics of climbing, including the forces at play and the equations that describe them, such as lift, weight, thrust, and drag. It also introduces the concept of the angle of climb and how it can be calculated using the excess thrust over weight, with examples provided to illustrate the calculations.

05:01

🔍 Climb Gradient and Its Influencing Factors

The second paragraph explores the climb gradient, which is the vertical change over the horizontal distance, and how it relates to the angle of climb. It explains that the climb gradient is influenced by the excess thrust over weight, and factors such as mass, aircraft configuration, altitude, temperature, and engine failure can affect this gradient. The paragraph also clarifies the difference between the climb angle and the flight path angle, using the analogy of a train and a moving air mass to illustrate how wind can affect the perceived climb angle relative to the ground, but not the actual climb angle relative to the air mass.

10:03

📈 Maximizing Climb Performance Through Excess Thrust and Power

This paragraph focuses on maximizing the angle of climb and the rate of climb by understanding the relationship between excess thrust and excess power. It discusses the concept of VX, the speed for the best angle of climb, and VY, the speed for the best rate of climb, explaining how these speeds relate to the aircraft's performance. The paragraph also covers how factors such as mass, aircraft configuration, altitude, temperature, and engine failure impact the rate of climb. It emphasizes the importance of excess power in achieving a higher rate of climb and how environmental factors and aircraft conditions can either aid or hinder this performance.

15:05

🚀 Climb Speeds and Their Impact on Aircraft Performance

The fourth paragraph delves deeper into the impact of various speeds on aircraft performance during the climb. It explains how increasing mass, aircraft configuration, altitude, and temperature affect the power available and required, thus influencing the rate of climb. The paragraph also discusses the theoretical maximum altitude an aircraft can reach, known as the absolute ceiling, and the service ceiling, which is a practical limit set below the absolute ceiling for safety. It touches on the importance of monitoring both indicated airspeed and Mach number during a climb to ensure the aircraft remains within safe operating limits.

20:06

✈️ Climbing Techniques and Safety Considerations

The final paragraph summarizes the key points about climbing techniques and the importance of safety considerations during the climb. It reiterates the significance of excess thrust and power in determining the climb angle and rate, and how factors like mass, thrust, drag, and environmental conditions can affect these. The paragraph also highlights the need to monitor airspeed and Mach number, especially when climbing at constant indicated airspeed, to avoid exceeding the aircraft's structural limits. It concludes with a simple mnemonic to remember the relationship between indicated airspeed, true airspeed, and Mach number during a climb.

Keywords

💡Climb Procedure

The climb procedure is the process an aircraft follows after takeoff to ascend to its cruising altitude. It's a critical phase of flight that involves managing the aircraft's performance to safely clear any obstacles and achieve the desired altitude. In the script, the climb procedure is discussed in the context of understanding the various factors that affect the steepness of the climb, such as angle of climb and rate of climb.

💡Angle of Climb

The angle of climb refers to the angle between the aircraft's flight path and the horizontal plane during ascent. It is a measure of how steeply an aircraft can climb and is determined by the balance of forces acting on the aircraft, specifically the excess thrust over weight. The script explains that the angle of climb can be calculated using the sine of the angle, which is equal to the excess thrust over the aircraft's weight.

💡Rate of Climb

The rate of climb is the measure of the vertical speed of an aircraft in its ascent, typically measured in feet per minute. It is influenced by the aircraft's speed, angle of climb, and the excess power available. The script discusses how the rate of climb is maximized at a specific airspeed known as VY, where the difference between power available and power required is the greatest.

💡Excess Thrust

Excess thrust is the difference between the thrust produced by the aircraft's engines and the drag acting against the aircraft. It is a key factor in determining both the angle of climb and the rate of climb. The script emphasizes that a larger excess thrust results in a steeper angle of climb and a higher rate of climb.

💡Climb Gradient

The climb gradient is the ratio of the vertical distance climbed to the horizontal distance traveled, essentially the steepness of the climb. It is closely related to the angle of climb, and for small angles, the sine of the angle of climb is approximately equal to the climb gradient. The script uses the climb gradient to illustrate the relationship between the angle of climb and the vertical change over horizontal distance.

💡VX and VY

VX and VY are specific airspeeds at which an aircraft achieves the best angle of climb and the best rate of climb, respectively. VX is the speed for maximum angle of climb, and VY is the speed for maximum rate of climb. The script explains that these speeds are determined by the point where excess thrust or excess power is maximized, which varies depending on the type of aircraft.

💡Environmental Factors

Environmental factors such as altitude, temperature, and wind can significantly affect an aircraft's climb performance. Higher altitudes and temperatures result in less dense air, reducing engine thrust and thus the aircraft's climb capabilities. The script discusses how these factors influence the climb gradient and rate of climb, and how pilots must adapt their climb procedures accordingly.

💡Multi-Engine Aircraft

A multi-engine aircraft has more than one engine, and the loss of one engine can significantly impact the climb performance. The script mentions that an engine failure results in a loss of thrust and an increase in drag, particularly if the failed engine's propeller is windmilling, leading to a reduced climb angle and rate of climb.

💡Flight Path Angle

The flight path angle is the angle between the aircraft's flight path and the ground. Unlike the climb angle, which is relative to the air mass, the flight path angle is affected by wind. The script uses a train analogy to explain the difference between the climb angle and the flight path angle, demonstrating how wind can alter the flight path angle while the climb angle remains the same.

💡Absolute Ceiling

The absolute ceiling is the highest altitude at which an aircraft can maintain a positive rate of climb, typically defined as the point where the rate of climb falls to zero feet per minute. The script explains that the absolute ceiling is influenced by factors such as engine thrust, which decreases with altitude due to reduced air density.

💡Service Ceiling

The service ceiling is a lower altitude than the absolute ceiling at which an aircraft can still achieve a specific rate of climb, such as 100 or 500 feet per minute, depending on the type of aircraft. The script mentions the service ceiling as a practical limit for aircraft operations, providing a buffer below the absolute ceiling.

Highlights

Introduction to the sixth class in the Performance Series focusing on the climb procedure.

Explanation of environmental factors affecting the steepness of the climb.

Climb phase begins after takeoff and can occur at various points in the flight.

Differentiating between angle of climb and rate of climb for safety and efficiency.

Force analysis during a steady climb with lift, weight, thrust, and drag.

Calculating the angle of climb using the sine of the angle and excess thrust.

Demonstration of how to find the angle of climb with given thrust and weight values.

Understanding the relationship between small angles, sine, and climb gradient.

Trigonometric conversion of angle to gradient for practical climbing scenarios.

Definition and importance of VX, the speed for the best angle of climb.

Differences in determining VX for jet and propeller-driven aircraft.

Factors influencing the angle of climb including mass, configuration, altitude, and temperature.

Impact of engine failure on climb performance in multi-engine aircraft.

Clarification of the difference between climb angle and flight path angle.

Explanation of how wind affects flight path angle but not climb angle.

Linear relationship between the angle of climb and the rate of climb at low angles.

Derivation of the rate of climb equation from excess power over weight.

Identification of VY, the speed for the best rate of climb, and its significance.

Factors affecting the rate of climb including mass, aircraft configuration, and environmental conditions.

The concept of absolute ceiling and service ceiling in relation to climb performance.

Climbing at constant indicated airspeed and its effect on true airspeed and Mach number.

Safety practices for climbing by using a combination of indicated airspeed and Mach number.

Transcripts

after we take off we settle into the

climb up to our cruising altitude but

what sort of performance characteristics

do we need to achieve on the way up

there

let's find out

[Music]

hi I'm Grant and welcome to the sixth

class in the performance Series today

we're going to be taking a look at the

climb procedure there's various external

environmental factors that will affect

how steep our climb is so we're best off

understanding them so we know if we'll

be able to safely climb above any

obstacles that are in our way the claim

phase of flight starts after the takeoff

has been completed and we pass the

screen height basically up to the

altitude we're going to cruise at but we

can also climb on route or after I go

around for example so it's not exclusive

to just after takeoff

when we're climbing the aircraft we

usually break it down either into an

angle of client that we need to achieve

say there's a mountain off the end of

the runway that we need to get over or a

certain rate of climb imagine there's an

aircraft closing in on us at the same

level we need to be able to climb fast

enough to clear it in time we're going

to start off by taking a look at the

angle of climb in a steady climb this is

what the forces look like we have lift

equal to weight times cosine Theta and

we have thrust equal to drag plus wait

times sine Theta we have thrust which is

larger than drag and weight which is

larger than lift

if we didn't know the angle we could

work it out if we knew all the other

factors by rearranging one of the

equations to look like this

basically it equates to any excess

thrust that we have so we can say that

sine theta equals the excess thrust

overweight if we have much more thrust

and a lot less drag making our excess

thrust larger then we would get a larger

number over here as a result sorry over

here as a result and a larger value for

sine Theta which equates to a larger

steeper angle so if we plug in some

numbers let's say we have a thousand

Newtons of extra thrust

over our aircraft which weighs 10 000

Newtons

then our sine Theta value

is going to be equal to

0.1 because that's a tenth of that

then if we take the inverse sine

of that that means that we can find out

the actual angle

then we will get the actual angle equal

to

5.7 degrees

if we had 2 000 Newtons of extra thrust

that'd be 0.2 and that equals 11.5 just

to give you a flavor for how this works

at small angles that are normally

experienced in aviation basically the

reason because it's only small angles is

because there's only ever a little bit

of extra thrust available there's never

that much extra thrust available so this

number rarely gets it rarely gets that

high

but basically when we're considering

small angles sine Theta roughly equals

the gradient of a climb the vertical

change over the horizontal

in the example four we get an angle of

5.7 degrees which we if we convert

into a gradient using trigonometry we'll

see why these two angles are similar

so let's see

using trigonometry that tan five point

seven equals the if we had our triangle

we have the angle in here we've got the

vertical which is the opposite over the

adjacent which is the horizontal

vertical over horizontal is gradient So

Tan 5.7 equals vertical over horizontal

and let's say we've covered a hundred

meters horizontally

that means that if we rearrange we're

trying to find the vertical

if we do the vertical

equal to tan 5.7 multiplied by 100

then

we can see the vertical change

if you calculate that out will be

9.98 meters which makes our gradient

vertical over the horizontal or tan

value would be 9.98 over 100

or we could say it's roughly 10 over 100

which is roughly

well

a bit of rounding our gradient is 0.1 so

by using that trigonometry we can see

that the value for sine Theta is

basically the same as the gradient

so what we can do is we can

re-jig this equation and say that sine

Theta is equal to the

climb gradient

so client gradient equals sine Theta

which also equals thrustmaster drag over

weight so the client gradient

equals excess thrust overweight VX is

one of many V speeds and this one stands

for the speed that we fly to achieve the

best angle of climb or the best climb

gradient

the best angle we know will occur where

excess thrust is maximized this happens

where we have the largest difference

between thrust and drag so we look at

the total drag curve with the thrust

available overlaid we can actually

figure out where this happens

for a turbojet aircraft it occurs here

at the bottom of the drag curve because

this is where we have the largest gap

the largest amount of excess thrust and

this is our speed for minimum drag this

is vmd

so in a jet aircraft vmd equals

the same as VX our speed for best client

in a propeller driven aircraft it's

slightly different we have vmd over here

but that's not actually the largest gap

the largest gap occurs

slower than vmd

and that's actually fairly close to the

speed for minimum power VMP

and the rvx speed again just without the

gaps the biggest nice and easy so

there's quite a few things that will

influence the angle of our climb or the

climb gradient but the thing that's key

is excess thrust so anything which

increases drag will be bad anything

which reduces thrust will be bad and

anything that increases thrust and

reduces drag will be good for that angle

allow us to apply a steeper angle

basically Mass we'll start with mass

mass increasing means in our equation

for climb gradient we're dividing by a

larger number which makes the climb

gradient smaller simple mathematics

would get a lower climb angle aircraft

configuration basically flaps and the

landing gear will mean more drag

that means a lower excess amount of

thrust

that excess thrust if you think about it

in terms of lines you would have uh uh

larger my drag that line for the total

drag curve would move up smaller Gap

again Lower climb gradient as a result

altitude increasing as we know from

class 4 on thrust means we have lower

air density and less thrust is produced

as a result

that means there's less excess rust and

that means that we can't climb

um as steep as we'd like so as thrust

goes down with increasing altitude our

climb gradient would also go down

temperature increasing has a very

similar effect to altitude as the

altitude increase sorry as the

temperature increases that means we're

in less tense air which produces less

thrust output so as the temperature goes

up less excess thrust we can't climb

steep we have a smaller climb gradient

on multi-engine aircraft if one of our

engines fail then we lose a large amount

of thrust therefore we lose a large

amount of excess thrust and if you

combine this with the increase in drag

caused by maybe a wind Milling propeller

or a deflected Rudder being used to keep

us straight then we get a large

reduction in excess thrust and we get

very reduced climb performance in terms

of the angle wind will not affect the

climb angle but will reflect something

called the flight path angle

the flight path angle is the aircraft

position relative to the ground and the

climb angle is the aircraft's position

relative to the air mass not the ground

which does sound a bit confusing but I

like to think of it as a train just bear

with me for a second hopefully it'll

make sense

stay where say we are in a train station

not moving that's this first example

here then if I walked up a slope ladder

resting at 45 degrees against the front

of the train Carriage carrying a toy

airplane the toy airplanes climb angle

would be 45 degrees and the overall

position relative to the ground the

flight path angle would also be 45

degrees it's

climbed there the ladder with me

um in the stationary train

so then we climbed down the ladder and

the train starts to move it starts to

reverse a little bit

we climb up the ladder again with a

climb angle of 45 degrees we're going

straight up the ladder but the position

of the toy airplane and US relative to

the train station or relative to the

ground has moved because as a whole the

train has been moving backwards so the

angle would be a lot steeper in this

case it's actually backwards just the

way I've drawn it then the train or the

air mass starts to move forward imagine

the trains being pushed by a Tailwind

for example

we climb down and then climb up again

the 45 degree ladder with the toy plane

The Climb angle relative to the air mass

or the train Carriage remains 45 degrees

but relative to the ground it's going to

be a lot shallower because the whole

thing has moved across it's pushed us

along

um relative to the ground so whilst The

Climb angle might be 45 degrees the

flight path angle will be a lot

shallower

so the claim angle isn't affected by

wind it's only the flight path angle in

cases where there's no wind

such as the starting condition the

flight path angle and the flight angle

will be the same but when there's wind

to consider the flight path angle and

the

climb angle will be different even I'm

getting confused seeing it but yeah

hopefully that train analogy works the

rate of climb or the rate of vertical

change will be larger for larger angles

of climb and at low angles that we

normally climb at the relationship is

fairly linear if we double the angle we

would double the rate of climb also if

we fly at a faster speed up the slope of

the climb then we would increase the

rate of climb we're covering more

vertical distance per second for example

that basically means that the rate of

climb depends on both the angle and the

true air speed that we fly up the slope

so if we take our equation that we know

for angle of climb and multiply it by

the true air speed we can extend it out

and see some interesting things so

that's the midpoint and then we multiply

the thrust by the trigger speed and the

drag by the trigger speed divide that

all by the weight and what we can do is

we can use our knowledge of thrust and

power to say that the thrust times the

true air speed is the power

available

and the drag times the trigger speed is

the power required so what's the

difference between power required and

power available well that would be

Excess power so the rate of climb

equals Excess power over weight very

similar to climb

but we're doing the angle over time and

power is essentially

um

thrust over time so that's the way would

be easy to remember it VY is another V

speed and this one stands for the speed

for the best rate of climb

the best rate we know will occur where

Excess power is maximized but we have

the largest difference between power

available and power required

so if we look at a power available

versus Power required graph for a jet we

can speak see that the speed for v y

occurs around about here that'd be where

the largest gap is between the two lines

and that is both faster than vmd which

equals VX in the case of a jet and also

the speed for minimum power when we look

at the graph for a propeller driven

aircraft we can see that the largest

difference between the power available

and the power required occurs in this

region here in between these two lines

it's actually usually a bit closer

weighted to vmd but it will be faster

always than VMP and VX as well so just

like with the angle there's various

things that influence the rate of climb

various environmental factors but the

key thing is Excess power for angle it's

excess thrust for rate it's Excess power

so simply put anything that reduces

thrust will be bad anything that

increases drag will be bad just as it

was for angle

so Mass increasing

will basically mean that we're dividing

by a larger number we got a lower rate

of climb nice and easy to understand but

if we think about it on the power

available versus Power required graph we

still have the same amount of power

available thrust times to your speed but

because we're heavier we need more lift

this causes an increase in induced drag

and therefore our total drag curve would

move up and to the right if we multiply

all the points on that new Total drag

curve by the Trier speed we will get a

new power required curve which also

moves up and to the right I've drawn

these lines a bit weird but basically it

means that we have a smaller gap between

the heavy aircraft and the power

available

when compared to the light aircraft and

the power available graph and it also

means because everything is heavier and

because the lines have moved up and to

the right it means that our speeds would

be faster so all speeds would increase

so VY is going to be faster for the

heavier aircraft when compared to this

one

it's the same with VX and all the speeds

in general if you're heavier you need

more lifts you need to fly faster no

matter what you're doing aircraft

configuration flaps and gear will

increase Dragon aircraft if we have more

drag on the aircraft if we multiply it

by the true air speed we get a larger

amount of power required Shifting the

overall line upwards therefore reducing

the gap between power available and

power required and we get a lower rate

of client as a result as we increase in

altitude we know that the thrust output

of the engines is reduced due to that

reducing density meaning that as we

multiply it by the true air speed we get

a much shallower line for power

available in a jet and this means a

lower smaller gap between the

and power available and power required

and as we get higher and higher the

power available lighting will continue

to shallow off and when we get to the

point where the two lines cross over

something like that

then we now require more thrust than we

have available and we've hit the

theoretical maximum altitude of the

aircraft which is known as the absolute

ceiling or in other words it's where the

rate of climb is zero feet per minute we

use feet per minute when we're talking

about rate of climates the units we also

um have an altitude which we call the

service ceiling this is slightly lower

than the absolute ceiling basically to

give a bit of a buffer uh in uh jet this

is when it's 500 feet per minute that's

the maximum amount of climb that we can

achieve when we're in a propeller it's a

hundred feet per minute temperature

increasing has the same effect as

altitude increasing less dense air less

stress to help us climb at a fast rate

basically imagine the line shallowing

off just as it has for altitude

increasing on multi-engine aircraft if

one of our engines fail then we lose a

large amount of thrust or

um Power available

and we also increase the drag due to the

windmill and propeller or the deflected

Rudder and we get a large increase in

the power required as a result that

means less XX Excess power overall and a

lower rate of climb as a result wind

doesn't affect the rate of climb

basically the rate of climb is the

vertical change

that we're concerned about and wind only

really acts in the horizontal plane so

it's not affecting the vertical plane

simple as that so in terms of claim

speeds we have VX for angle and v y for

rate simple as that well not really

hence all the other stuff on the page

but

if we fly using an indicator speed which

is what we normally do in front of us

using the dials and displays that

actually show us our indicator speed

then if we climb the true air speed will

increase above the indicator speed if we

climb with a constant indicator speed

sorry the true air speed will start to

increase above the indicator speed as we

get higher and higher basically because

of this equation

if we are flying with a constant

indicate air speed this stops reducing

then it means that the Tas has to rise

as a result to keep our indicator speed

constant

this will result in the Mach number also

increasing so as the task is increasing

Mach number is going to go up as well

and to be climb it gets colder local

speed design goes down leading to the

Mach number and increasing quite a lot

this could lead to over speeding the

aircraft above structural limits which

are normally given as a Mach number this

MMO Mach number maximum operating

in Jets at least

so what we do if we're going to climb at

the constant indicator speed we'd run

into this problem so what we do is we

climb using both a combination of

indicated AirSpeed calibrator speed or

equivalent AirSpeed whatever you want to

call it and Mach number

and we do

a change over at a certain change over

altitude where we stop climbing at a

constant indicate AirSpeed and then

start climbing at a constant Mac speed

you can see I've made a little mistake

here obviously the lines

line up with the equivalent speeds that

they're supposed to be lined up with so

by climbing up this constant Mach number

we keep ourselves safe from this maximum

uh operating Mach number and you might

see some questions in the exam asking

you about the different climbing speeds

and certain types of speed the easy way

to remember it is basically with these

three fingers on your left hand I make

sense for me because I'm right-handed so

the spear hand is the one I've got look

inside your hand the middle finger is

the Mach number

some numbers that indicate air speed and

the index finger is the true air speed

so you've got it

you know it and Mach number for the

middle whichever is constant goes

straight up and you can see what happens

to others so for example if we climb a

constant indicate air speed

the Taz and the Mach number both go up

then we switch over to the Mach number

we can see the Taz and the indicated

AirSpeed start to reduce

simple to summarize climbing then climb

gradient is given by the equation excess

thrust overweight and we got there by

rearranging the forces in a climb so

that we had sine theta equals thrust

minus drag over weight and if we were to

find the angle we would take the the

inverse sine of the result on this side

but for small angles sine Theta roughly

equals tan Theta

and tantia is the same as the gradient

the vertical change over the horizontal

change so we can say that tan Theta or

the gradient is equal to excess thrust

overweight

to maximize the gradient and the angle

we want to maximize this value over here

which means either maximizing excess

thrust

or minimizing weight

so if we have more mass we would have a

smaller angle if we have less Mass we

have a larger angle

if we have more thrust

and or less thrust that would mean less

excess thrust things that cause less

thrust would be an engine failing for

example they usually get a lot less

thrust increasing altitude causes a

reduction in thrust and increasing

temperature also causes a reduction in

thrust causing a reduction in excess

thrust which means that climb angle is

smaller client gradient is smaller

anything which increases drag will also

reduce the excess thrust think about

flaps think about gear think about

things like contamination on the

aircraft like ice Frost that kind of

stuff that'll increase drag which will

reduce excess thrust

reduce excess thrust and reduce the

angle so whereas

climb angle is all about excess thrust

rate of climb is all about Excess power

and we need to maximize Excess power if

we want to maximize our rate of climb

it's basically the same things as we do

for angle we want more thrust less drag

and less weight to achieve a faster rate

of climb and we do this by reducing the

weight that's a simple one and if we are

at low altitudes with uh more thrust

available then we'd climb faster and if

we've got low drag then again we'd climb

faster because we have more Excess power

available

um things like wind don't affect the

rate of climb because rate of climb is

to do with vertical change not

horizontal change where wind is

concerned and with climb actually never

talked about wind but think of that

train analogy the wind doesn't actually

change the angle

um of the climb just the flight path

angle the angle relative to the ground

so as we climb if we climb with a

constant indicated air speed the trigger

speed and the Mach number increase up to

the limiting speeds of the aircraft so

we have to climb with a combination of

both indicated air speed and Mach number

and basically we do that the change over

altitude we switch from indicator speed

to Mach number to make sure the trigger

speed and the indicator speeds remain in

safe sort of ranges and the Mach number

more importantly stays in the safe range