good morning friends in the last lecture and
also in coming few lectures i will be just
sharing few philosophy few do's and don'ts
before we start rigorously following a procedure
to design an aircraft in the last lecture
i showed you that for the preliminary stage
when our student the design aero models ah
remote driven by thumb rule and few things
are heuristic as well and that's exactly why
i said that please do not bring those thing
with you when you attend my lecture but truly
speaking if you find somebody is really a
passionate aero modeler he is feeling for
numbers are huge you have to respect an aero
modeler truly aero modeler i work with few
of them captain amoolya captain mukherjee
and huge number of things i am learned from
them only you as it participant of this course
should realize that the feel of an aero modeler
truly aero modeler he may not be able to explain
the law of aerodynamics the way you want but
if we have learn this course you should be
able to translate his feel into number a radio
procedure based on scientific assumptions
so that is where the aero modeler and this
course will merge but not at this stage after
we build up our self as appropriate time i
will bring a aero modeler what is respectful
aero modeler and share some some thoughts
with him to prove my ah point ok
we will still continue on few things which
will be useful and it is also a part of revision
we have seen that we have been talking about
w by s we have been talking about t by w and
when it comes to t by w how much t by w is
required but in normal say cruise dominating
airplane if i want to really see that then
i know that t equal to d and l equal to w
that means t by w is one by c l by c d if
i write t by w cruise equal to one by c l
by c d so what is the t by w required for
cruise how do i [an/answer] answer that means
i need to know at what c l by c d i am cruising
for example if i am cruising such that drag
is minimum it's an cursing such that drag
is minimum then i know that for this condition
c l by c d has to be maximum and that means
c l has to be c d naught by k this number
so immediately i know t by w will be one by
c l by c d and let us say c l by c d max this
value when i write t by w cruise i say cruise
for minimum t by w that means c l by c d is
maximum that means drag is minimum so i know
that value t by w as one by c l by c d max
which corresponds to the c l equal to c d
naught by k
typically c l by c d max could be fifteen
one number i am writing so it could see immediately
t by w cruise is one by fifteen ok but here
you should understand this t by w cruise is
one by fifteen this is not equal to t by w
takeoff why for two reason that for t by w
takeoff we need to have a different criteria
for t by w takeoff we have seen that if i
write t minus d minus w sin gamma and if i
am to takeoff without any acceleration that
is steady climbs small climb i am doing then
t by w is roughly equal to w sin gamma plus
one by c l by c d we have shown the roughly
this is approximately
so t by w takeoff would be more governed by
this part the climb angle gamma t by w cruise
will be more driven by c l by c d max right
so if i am a designer i immediately know what
is by t by w cruise required because i know
roughly it will be c l by c d ten or fifteen
whatever way i am designing so i know t by
w cruise i required this much one by fifteen
and t by w takeoff how much is required one
way do get it is ok if i am trying to climb
at some angle fifteen degree climb angle twenty
degree climb angle so i can easily see here
of course this w will not be here this w will
not be here yes right directly proportional
to sin gamma but you also understand this
t by w will play important role during takeoff
also takeoff means that phase that is from
start to a speed were we takeoff has been
achieved if i want to shrink in this length
before it get's the we takeoff speed i have
to accelerate the airplane faster if i want
to reduce this length that means if i have
the really reduce this length then t by w
has to be very high because t by w will decide
how much active force is applied to accelerate
the body or the airplane this case from zero
to we takeoff so t by w will play role here
t by w will play role here cruise what is
the t by w require t by w for climb also without
going into detail you know if you want to
go for a turn high rate of turn t by w also
will play a role there we will see as we revolve
step by step this is one we should be very
very clear
when i am mentioning all this thing is the
one point you should understand when you are
designing an airplane we cannot a specify
like t by w cruise i want this much t by w
takeoff i want this much t by w some acceleration
parameter i want this much because why because
notice that if t by w cruise is fifteen and
if i want to know what should be t by w where
from i should start then that it will be different
than this value because i want t by w cruise
some number now what is happening as it is
going from here to here the weight is going
on reducing because where is being consumed
so what is a better approaches we if we know
how much fuel is consumed then modify this
weight here that is i have to increase this
weight and we talk in terms of t by w takeoff
this is important every such ratios with weight
will be converting back into w takeoff that
should be kept in your mind ok and the reason
is very simple that if i say t by w cruise
is some number i know that that w is not w
takeoff but finally as a designer i want to
know what is the w takeoff required that is
where from i start so that's why always it
is advisable you convert this number any number
which is divided by w convert it to w takeoff
by appropriately adjusting the weight most
of the cases it is because of fuel consumption
and that's not a very difficult task we will
be doing that there is a procedure doing that
so this was one thing i thought i must share
with you before you start using them another
important parameter you will find when i am
talking about c l by c d max sometime we remember
for power we talk about c l three by two by
c d max
let us again go back to performance i am talking
in terms of range and endurance that will
be one of our ah important parameter performance
parameter so if i go back you remember that
c l for minimum drag the condition was c l
equal to c d naught by k and c l for minimum
power or equal to three c d naught by k so
another purpose of writing all this thing
is that to give enough time you go back and
revise all those things so that you are prepared
for application of this understanding in terms
of synthesizing a design synthesizing concept
to get a conceptual design ok if it is c l
minimum for minimum drag i mean c l required
for a minimum drag is c d naught by k and
you know that this is discussed call to c
l by c d maximum and this corresponds to c
l three by two by c d maximum remember ok
now let us see we will play around with this
so if if i write now c d equal to c d naught
plus k c l square so if i write now c d for
minimum drag is c d naught plus k c d for
minimum drag is this one so this will become
c d naught by k so this will become two c
d naught so c d for minimum drag is to c d
naught this is nothing new for you similarly
c d for minimum power will be c d naught plus
k in to c l square means three c d naught
by k so this is equal to four c d naught please
notice this that c d for minimum power is
twice the c d naught and c d for minimum power
is four c d naught ok
so obviously v for a minimum power will be
because after we flying lift equal to weight
that implies v equal to under root two w by
s rho c l so v for minimum power will be what
you know v for minimum power means c l is
three c d naught by k so i write it as under
root two w by s rho under root three c d naught
by k so that will be your let me write here
so that things are clear that will be ah two
w by s rho under root three c d naught by
k this is what is here right similarly v for
minimum drag these are straight forward for
you all know all this things this only will
help you to go back and revise the nodes so
that whenever i take some assumption you understand
what i am doing there is no objection here
now let us say with this if i now try to find
out which case the drag will be more why we
are asking this question we are trying to
find out finally c d is here and drag means
when i talk about drag this is dynamic pressure
that will half rho v square s into c d right
one thing is clear when i am flying at c l
is equal to under root three c d naught by
k which is a minimum power case to maintain
lift equal to weight at same altitude i will
be flying slower because c l will be higher
compared to c l required for minimum brackets
right so the dynamic pressure for this case
for minimum power case will be less as for
dynamic pressure is concerned i can write
dynamic pressure corresponding to minimum
power will be less compared to dynamic pressure
for minimum drag no objection in this because
the c l for a minimum power is higher as compare
to c l for minimum drag so the speed for minimum
power will be lesser compare to c l for minimum
drag to maintain the same weight the lift
equal to weight natural dynamic pressure which
is half rho v square if both the things we
have comparing at same altitude so dynamic
pressure for minimum power will be less than
dynamic pressure that minimum drag so drag
minimum power will be half rho v square for
v i will write two w by s rho three c d naught
by k and drag for minimum drag case as is
l by d maximum in this case l by d is maximum
that will be half rho two w by s rho into
under root c d naught by k if i ask a question
in which case drag will be more let us find
out if we take the ratio between this two
i can write d minimum power by d minimum drag
this will be will be equal to two by root
three you see how it is happening i have miss
some point here so drag minimum power will
be half rho v square into s into c d how much
was c d for minimum power for the minimum
power c d was four c d naught we have shown
that severally here i missed s into two c
d naught right because we have seen c d for
minimum power is four c d naught and c d for
minimum drag is two c d naught we just we
have shown that right
so now if i take the ratio we will find these
two everything will get cancelled four and
two so the two remain there and root three
root three will be there right do it yourself
for this ratio will be roughly two by one
point seven three two and this is equal to
one point one five four seven so as a designer
we say drag during minimum power condition
is fifteen percent more than l by d maximum
case right you can see that drag during minimum
power is fifteen percent roughly more than
the drag during l by d max case right how
that is important let us see now a designer
interpretation how a designer evaluate utilize
this that is very important if drag is increased
by fifteen percent for minimum power case
right minimum power case here means suppose
this is a case were c l three by two by c
d is maximum with that we are going on and
we know how c l three by two by c d s come
you can refer back your lecture if that is
true that means c l by c d if drag rises fifteen
percent then i can write c l by c d as one
by one point one five which is come from here
the ratio of this two is one point one five
four seven which is equal to point eight six
six l by d max this is part clear what how
a designer is utilizing this relationship
says drag during minimum power is fifteen
percent more than the drag if we are flying
at minimum drag so c l by c d will be now
modified because c d has increased by fifteen
percent and this one by one point five so
that gives point eight six six l by d max
with this understanding we will fix our initial
design parameters for example which will be
which will have relevance for range and endurance
if we recall if i take jet and it prop i am
talking about range and endurance which is
also called loiter which is point eight six
six l by d max and here it is l by d max and
here it is l by d max here it is point eight
six six l by d max for it is connect if you
see the expression for range for a jet driven
airplane the condition for range maximum range
is c l three by two by c d should be maximum
so which is like a minimum power conditions
equivalently and you know for c l three by
two by c d if i take that we will have seen
c l by c d should be point eight eight six
six of l by d max but for endurance for a
jet a airplane it will be maximum when l by
d is max so i am putting is l by d max for
a propeller it is other way for maximum range
the condition says it should fly such that
l by d should be maximum and for endurance
it should be c l three by two by c d that
condition it gives point eight six l by d
max you must be wondering i have not so for
announce the books textbook i will be using
i will be doing that in the next class i will
be follow it two three books so mostly one
book which i will be following initial part
is reimar aircraft design by reimer which
must be going on the most popular book but
i will formally give you the volume etcetera
addition and please understand why we are
doing all those revision because for an aircraft
designer what will be the weight of the airplane
is a big question how do i know how much is
the weight luckily our situation is not situation
of during right by those time with there were
no historical data right
ok see how great they were say i always say
from right brothers so much of aircraft why
we could not design a good civilian aircraft
one of my friend told they had right brothers
we have brothers per have they are not right
they are wrong and that is the my motivation
for this lecture series that after this lecture
at least we have initiated a process creating
a right brothers among the wrong brothers
and among the wrong brothers i am one of those
wrong brothers because i am also i have failed
to design in civilian good aircraft main issue
comes on the weight of the airplane say now
the situation in little different whenever
you think about the aircraft lets a civilian
aircraft first question comes what sort of
a range you are talking about short range
or long range aircraft then comes what sort
of a number of passenger should talking about
and what sort of a speed you are talking about
fortunately whatever you think you will find
some of that class is there so you have got
lot of database
now so it is very easy to select a baseline
aircraft for the mission what you are looking
for closer to that from there are you can
easily get some number ok my aircraft will
be this weight class right when i am saying
this please understand what i am trying to
tell you is we will be using lot of historical
data to get the initial numbers for example
if this is w naught gross weight of the airplane
it will be composed of now you call it build
up method weight build up method we will break
it into different different components for
example weight of crew we know weight of payload
we will be knowing how many passenger or any
other military payload then weight of fuel
and you say empty weight this is very important
empty weight and if i now see here out of
this four this is under my hand i know a priority
this a priory i know but w f which is the
fuel weight and w e is the empty weight these
are to be carefully find out and there will
be using lot of historical data if you see
now if i rearrange this i can write w naught
or it's say if i write w f either function
of w f by w naught into w naught and w e as
w e by w naught into w naught what is the
meaning of this that based on the historical
data if i know this ratio w f by w naught
based on the historical data if i know w e
by w naught then my life will be simpler and
the statistical data whatever is available
they are being made available in this fashion
so that becomes easier for us to ah use for
to get initial gross weight another point
you should understand w f which is the fuel
weight it will be direct function of what
sort of mission you have got you have a takeoff
cruise you may accelerate dive you may again
go up so many things possible you may loiter
so depending upon type of mission requirement
so this is more driven by mission requirement
what is the mission of the airplane what are
the missions what sort of operation is supposed
to do what sort of manual supposed to do so
in the next class we will be starting from
here how do i get the initial weight estimates
using historical data right and also we will
be talking about mission profiles
thank you very much
