How do ground effect vehicles perform turns?What is ground effect?How come the ground effect has such a different outcome for wings and cars?What is the effect of uneven ground on ground effect vehicles?Why do aircraft need a vertical tailfin, but birds don't? (and lots of fish do?)Can we borrow Formula One's ground effect for airplanes?What are the effects of the tilted lift vector in a banked plane?How high does the ground effect last?What are the dynamic stability properties of an aircraft with wings exactly at the vertical CoG?How would a low-airspeed fixed-wing drone be designed to reduce effects from gusts and wind shear?Human-powered flight in vs. out of ground effect?
Russian word for a male zebra
Should I put programming books I wrote a few years ago on my resume?
Which is the better way to call a method that is only available to one class that implements an interface but not the other one?
How to hide rifle during medieval town entrance inspection?
Am I obliged to report rude/awkward language even if it doesn't offend me?
Ability To Change Root User Password (Vulnerability?)
What is exactly Avijja -- and how to uproot it?
What is the purpose of bonds within an investment portfolio?
Why Does Mama Coco Look Old After Going to the Other World?
Does putting salt first make it easier for attacker to bruteforce the hash?
Is using 'echo' to display attacker-controlled data on the terminal dangerous?
Explain the ending of Black Mirror's "Smithereens"
How can I remove material from this wood beam?
Excel division by 0 error when trying to average results of formulas
How can I deal with uncomfortable silence from my partner?
Why not invest in precious metals?
Is there a set of positive integers of density 1 which contains no infinite arithmetic progression?
Should I refuse being named as co-author of a bad quality paper?
Teaching a class likely meant to inflate the GPA of student athletes
Why am I Seeing A Weird "Notch" on the Data Line For Some Logical 1s?
Why does ''cat "$1:-/dev/stdin | ... &>/dev/null'' work in bash but not dash?
Proving that a Russian cryptographic standard is too structured
How to trick the reader into thinking they're following a redshirt instead of the protagonist?
How do free-speech protections in the United States apply in public to corporate misrepresentations?
How do ground effect vehicles perform turns?
What is ground effect?How come the ground effect has such a different outcome for wings and cars?What is the effect of uneven ground on ground effect vehicles?Why do aircraft need a vertical tailfin, but birds don't? (and lots of fish do?)Can we borrow Formula One's ground effect for airplanes?What are the effects of the tilted lift vector in a banked plane?How high does the ground effect last?What are the dynamic stability properties of an aircraft with wings exactly at the vertical CoG?How would a low-airspeed fixed-wing drone be designed to reduce effects from gusts and wind shear?Human-powered flight in vs. out of ground effect?
$begingroup$
Considering that Wing-In-Ground-Effect (WIGE) vehicles fly with a rather low ground clearance, there is not much room for banking. How do WIGE vehicles turn? Do they turn just very slow with a low bank angle? Or do they turn uncoordinated with wings level?
I can imagine that banking has an opposite effect: the raised wing has less ground effect so more drag so it creates some countering yaw moment. Is this correct?
aerodynamics ground-effect
edited Mar 25 at 11:17
Zeiss Ikon
4,147621
asked Mar 24 at 16:32
FlorianFlorian
2,1522829
$endgroup$
add a comment |
$begingroup$
Considering that Wing-In-Ground-Effect (WIGE) vehicles fly with a rather low ground clearance, there is not much room for banking. How do WIGE vehicles turn? Do they turn just very slow with a low bank angle? Or do they turn uncoordinated with wings level?
I can imagine that banking has an opposite effect: the raised wing has less ground effect so more drag so it creates some countering yaw moment. Is this correct?
aerodynamics ground-effect
edited Mar 25 at 11:17
Zeiss Ikon
4,147621
asked Mar 24 at 16:32
FlorianFlorian
2,1522829
$endgroup$
8
$begingroup$
"carefully" ....
$endgroup$
– Fattie
Mar 24 at 19:54
$begingroup$
Wouldn't the raised wing have less drag, because it's experiencing less ground effect, ergo producing less lift, ergo generating less induced drag?
$endgroup$
– Sean
Mar 25 at 2:51
2
$begingroup$
@Sean, no: the essence of the ground effect that you get more lift for the same drag. Or same lfit with less drag. Also, if you are in a sustained banked turn, then by definition both half-wings produce the same lift - otherwise you'd be rolling with acceleration. It follows that the surface that is less in ground effect will have more drag. (Plus there are usual effects due to ailerons position etc. - which usually contribute with the same sign).
$endgroup$
– Zeus
Mar 25 at 4:54
add a comment |
$begingroup$
Considering that Wing-In-Ground-Effect (WIGE) vehicles fly with a rather low ground clearance, there is not much room for banking. How do WIGE vehicles turn? Do they turn just very slow with a low bank angle? Or do they turn uncoordinated with wings level?
I can imagine that banking has an opposite effect: the raised wing has less ground effect so more drag so it creates some countering yaw moment. Is this correct?
aerodynamics ground-effect
edited Mar 25 at 11:17
Zeiss Ikon
4,147621
asked Mar 24 at 16:32
FlorianFlorian
2,1522829
$endgroup$
Considering that Wing-In-Ground-Effect (WIGE) vehicles fly with a rather low ground clearance, there is not much room for banking. How do WIGE vehicles turn? Do they turn just very slow with a low bank angle? Or do they turn uncoordinated with wings level?
I can imagine that banking has an opposite effect: the raised wing has less ground effect so more drag so it creates some countering yaw moment. Is this correct?
aerodynamics ground-effect
aerodynamics ground-effect
edited Mar 25 at 11:17
Zeiss Ikon
4,147621
asked Mar 24 at 16:32
FlorianFlorian
2,1522829
edited Mar 25 at 11:17
Zeiss Ikon
4,147621
asked Mar 24 at 16:32
FlorianFlorian
2,1522829
edited Mar 25 at 11:17
Zeiss Ikon
4,147621
edited Mar 25 at 11:17
Zeiss Ikon
4,147621
edited Mar 25 at 11:17
Zeiss Ikon
4,147621
4,147621
asked Mar 24 at 16:32
FlorianFlorian
2,1522829
asked Mar 24 at 16:32
FlorianFlorian
2,1522829
asked Mar 24 at 16:32
FlorianFlorian
2,1522829
2,1522829
8
$begingroup$
"carefully" ....
$endgroup$
– Fattie
Mar 24 at 19:54
$begingroup$
Wouldn't the raised wing have less drag, because it's experiencing less ground effect, ergo producing less lift, ergo generating less induced drag?
$endgroup$
– Sean
Mar 25 at 2:51
2
$begingroup$
@Sean, no: the essence of the ground effect that you get more lift for the same drag. Or same lfit with less drag. Also, if you are in a sustained banked turn, then by definition both half-wings produce the same lift - otherwise you'd be rolling with acceleration. It follows that the surface that is less in ground effect will have more drag. (Plus there are usual effects due to ailerons position etc. - which usually contribute with the same sign).
$endgroup$
– Zeus
Mar 25 at 4:54
add a comment |
8
$begingroup$
"carefully" ....
$endgroup$
– Fattie
Mar 24 at 19:54
$begingroup$
Wouldn't the raised wing have less drag, because it's experiencing less ground effect, ergo producing less lift, ergo generating less induced drag?
$endgroup$
– Sean
Mar 25 at 2:51
2
$begingroup$
@Sean, no: the essence of the ground effect that you get more lift for the same drag. Or same lfit with less drag. Also, if you are in a sustained banked turn, then by definition both half-wings produce the same lift - otherwise you'd be rolling with acceleration. It follows that the surface that is less in ground effect will have more drag. (Plus there are usual effects due to ailerons position etc. - which usually contribute with the same sign).
$endgroup$
– Zeus
Mar 25 at 4:54
8
8
$begingroup$
"carefully" ....
$endgroup$
– Fattie
Mar 24 at 19:54
$begingroup$
"carefully" ....
$endgroup$
– Fattie
Mar 24 at 19:54
$begingroup$
Wouldn't the raised wing have less drag, because it's experiencing less ground effect, ergo producing less lift, ergo generating less induced drag?
$endgroup$
– Sean
Mar 25 at 2:51
$begingroup$
Wouldn't the raised wing have less drag, because it's experiencing less ground effect, ergo producing less lift, ergo generating less induced drag?
$endgroup$
– Sean
Mar 25 at 2:51
2
2
$begingroup$
@Sean, no: the essence of the ground effect that you get more lift for the same drag. Or same lfit with less drag. Also, if you are in a sustained banked turn, then by definition both half-wings produce the same lift - otherwise you'd be rolling with acceleration. It follows that the surface that is less in ground effect will have more drag. (Plus there are usual effects due to ailerons position etc. - which usually contribute with the same sign).
$endgroup$
– Zeus
Mar 25 at 4:54
$begingroup$
@Sean, no: the essence of the ground effect that you get more lift for the same drag. Or same lfit with less drag. Also, if you are in a sustained banked turn, then by definition both half-wings produce the same lift - otherwise you'd be rolling with acceleration. It follows that the surface that is less in ground effect will have more drag. (Plus there are usual effects due to ailerons position etc. - which usually contribute with the same sign).
$endgroup$
– Zeus
Mar 25 at 4:54
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
It turns like an airplane by tilting the lift vector. Watch carefully in this video, especially about 50 seconds in, and you can see the craft is turning by banking.
It just can't bank very hard unless it climbs a little higher. This is one of the problems of GE aircraft; they aren't very maneuverable because they can only make gentle turns at the normal cruising level close to the surface.
The alternative to banking, if you don't have enough room to roll, is skidding, where you are redirecting the thrust vector and also generating some lateral force from the sideways presentation of the craft's body. Basically like a hovercraft. A lot less efficient though because of the drag rise from the skid. Some of those really big GE machines like the Ekranoplan would have used skidding (kind of obvious from the huge rudder that it's designed to skid) and maybe a little bit of bank.
It's probably a good thing that this concept has not been all that successful. If the world was full of these types of machines crisscrossing every which way over oceans and lakes, all at the same level and going pretty fast, you probably have a lot more mid-airs than you get with airplanes, or boat collisions for that matter.
edited Mar 25 at 8:32
ymb1
74k7241398
answered Mar 24 at 18:11
John KJohn K
31.2k152102
$endgroup$
$begingroup$
How did large versions like the Ekranoplan turn? Looks like there's a fairly large rudder, and engine thrust might have been used. There doesn't seem to be much margin for bank angle.
$endgroup$
– rcgldr
Mar 24 at 18:44
$begingroup$
It never occurred to me that such craft would indeed "meet" - just like ground vehicles! You'd need stop signs and so on.
$endgroup$
– Fattie
Mar 24 at 19:54
2
$begingroup$
@rcgldr thanks for the mention I added an extra paragraph to address that.
$endgroup$
– John K
Mar 24 at 20:01
1
$begingroup$
Stop signs on buoys! That would be rather funny, @Fattie!
$endgroup$
– FreeMan
Mar 25 at 12:34
$begingroup$
@FreeMan - right :)
$endgroup$
– Fattie
Mar 25 at 12:36
add a comment |
Your Answer
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "528"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2faviation.stackexchange.com%2fquestions%2f61572%2fhow-do-ground-effect-vehicles-perform-turns%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
It turns like an airplane by tilting the lift vector. Watch carefully in this video, especially about 50 seconds in, and you can see the craft is turning by banking.
It just can't bank very hard unless it climbs a little higher. This is one of the problems of GE aircraft; they aren't very maneuverable because they can only make gentle turns at the normal cruising level close to the surface.
The alternative to banking, if you don't have enough room to roll, is skidding, where you are redirecting the thrust vector and also generating some lateral force from the sideways presentation of the craft's body. Basically like a hovercraft. A lot less efficient though because of the drag rise from the skid. Some of those really big GE machines like the Ekranoplan would have used skidding (kind of obvious from the huge rudder that it's designed to skid) and maybe a little bit of bank.
It's probably a good thing that this concept has not been all that successful. If the world was full of these types of machines crisscrossing every which way over oceans and lakes, all at the same level and going pretty fast, you probably have a lot more mid-airs than you get with airplanes, or boat collisions for that matter.
edited Mar 25 at 8:32
ymb1
74k7241398
answered Mar 24 at 18:11
John KJohn K
31.2k152102
$endgroup$
$begingroup$
How did large versions like the Ekranoplan turn? Looks like there's a fairly large rudder, and engine thrust might have been used. There doesn't seem to be much margin for bank angle.
$endgroup$
– rcgldr
Mar 24 at 18:44
$begingroup$
It never occurred to me that such craft would indeed "meet" - just like ground vehicles! You'd need stop signs and so on.
$endgroup$
– Fattie
Mar 24 at 19:54
2
$begingroup$
@rcgldr thanks for the mention I added an extra paragraph to address that.
$endgroup$
– John K
Mar 24 at 20:01
1
$begingroup$
Stop signs on buoys! That would be rather funny, @Fattie!
$endgroup$
– FreeMan
Mar 25 at 12:34
$begingroup$
@FreeMan - right :)
$endgroup$
– Fattie
Mar 25 at 12:36
add a comment |
$begingroup$
It turns like an airplane by tilting the lift vector. Watch carefully in this video, especially about 50 seconds in, and you can see the craft is turning by banking.
It just can't bank very hard unless it climbs a little higher. This is one of the problems of GE aircraft; they aren't very maneuverable because they can only make gentle turns at the normal cruising level close to the surface.
The alternative to banking, if you don't have enough room to roll, is skidding, where you are redirecting the thrust vector and also generating some lateral force from the sideways presentation of the craft's body. Basically like a hovercraft. A lot less efficient though because of the drag rise from the skid. Some of those really big GE machines like the Ekranoplan would have used skidding (kind of obvious from the huge rudder that it's designed to skid) and maybe a little bit of bank.
It's probably a good thing that this concept has not been all that successful. If the world was full of these types of machines crisscrossing every which way over oceans and lakes, all at the same level and going pretty fast, you probably have a lot more mid-airs than you get with airplanes, or boat collisions for that matter.
edited Mar 25 at 8:32
ymb1
74k7241398
answered Mar 24 at 18:11
John KJohn K
31.2k152102
$endgroup$
$begingroup$
How did large versions like the Ekranoplan turn? Looks like there's a fairly large rudder, and engine thrust might have been used. There doesn't seem to be much margin for bank angle.
$endgroup$
– rcgldr
Mar 24 at 18:44
$begingroup$
It never occurred to me that such craft would indeed "meet" - just like ground vehicles! You'd need stop signs and so on.
$endgroup$
– Fattie
Mar 24 at 19:54
2
$begingroup$
@rcgldr thanks for the mention I added an extra paragraph to address that.
$endgroup$
– John K
Mar 24 at 20:01
1
$begingroup$
Stop signs on buoys! That would be rather funny, @Fattie!
$endgroup$
– FreeMan
Mar 25 at 12:34
$begingroup$
@FreeMan - right :)
$endgroup$
– Fattie
Mar 25 at 12:36
add a comment |
$begingroup$
It turns like an airplane by tilting the lift vector. Watch carefully in this video, especially about 50 seconds in, and you can see the craft is turning by banking.
It just can't bank very hard unless it climbs a little higher. This is one of the problems of GE aircraft; they aren't very maneuverable because they can only make gentle turns at the normal cruising level close to the surface.
The alternative to banking, if you don't have enough room to roll, is skidding, where you are redirecting the thrust vector and also generating some lateral force from the sideways presentation of the craft's body. Basically like a hovercraft. A lot less efficient though because of the drag rise from the skid. Some of those really big GE machines like the Ekranoplan would have used skidding (kind of obvious from the huge rudder that it's designed to skid) and maybe a little bit of bank.
It's probably a good thing that this concept has not been all that successful. If the world was full of these types of machines crisscrossing every which way over oceans and lakes, all at the same level and going pretty fast, you probably have a lot more mid-airs than you get with airplanes, or boat collisions for that matter.
edited Mar 25 at 8:32
ymb1
74k7241398
answered Mar 24 at 18:11
John KJohn K
31.2k152102
$endgroup$
It turns like an airplane by tilting the lift vector. Watch carefully in this video, especially about 50 seconds in, and you can see the craft is turning by banking.
It just can't bank very hard unless it climbs a little higher. This is one of the problems of GE aircraft; they aren't very maneuverable because they can only make gentle turns at the normal cruising level close to the surface.
The alternative to banking, if you don't have enough room to roll, is skidding, where you are redirecting the thrust vector and also generating some lateral force from the sideways presentation of the craft's body. Basically like a hovercraft. A lot less efficient though because of the drag rise from the skid. Some of those really big GE machines like the Ekranoplan would have used skidding (kind of obvious from the huge rudder that it's designed to skid) and maybe a little bit of bank.
It's probably a good thing that this concept has not been all that successful. If the world was full of these types of machines crisscrossing every which way over oceans and lakes, all at the same level and going pretty fast, you probably have a lot more mid-airs than you get with airplanes, or boat collisions for that matter.
edited Mar 25 at 8:32
ymb1
74k7241398
answered Mar 24 at 18:11
John KJohn K
31.2k152102
edited Mar 25 at 8:32
ymb1
74k7241398
edited Mar 25 at 8:32
ymb1
74k7241398
edited Mar 25 at 8:32
ymb1
74k7241398
74k7241398
answered Mar 24 at 18:11
John KJohn K
31.2k152102
answered Mar 24 at 18:11
John KJohn K
31.2k152102
answered Mar 24 at 18:11
John KJohn K
31.2k152102
31.2k152102
$begingroup$
How did large versions like the Ekranoplan turn? Looks like there's a fairly large rudder, and engine thrust might have been used. There doesn't seem to be much margin for bank angle.
$endgroup$
– rcgldr
Mar 24 at 18:44
$begingroup$
It never occurred to me that such craft would indeed "meet" - just like ground vehicles! You'd need stop signs and so on.
$endgroup$
– Fattie
Mar 24 at 19:54
2
$begingroup$
@rcgldr thanks for the mention I added an extra paragraph to address that.
$endgroup$
– John K
Mar 24 at 20:01
1
$begingroup$
Stop signs on buoys! That would be rather funny, @Fattie!
$endgroup$
– FreeMan
Mar 25 at 12:34
$begingroup$
@FreeMan - right :)
$endgroup$
– Fattie
Mar 25 at 12:36
add a comment |
$begingroup$
How did large versions like the Ekranoplan turn? Looks like there's a fairly large rudder, and engine thrust might have been used. There doesn't seem to be much margin for bank angle.
$endgroup$
– rcgldr
Mar 24 at 18:44
$begingroup$
It never occurred to me that such craft would indeed "meet" - just like ground vehicles! You'd need stop signs and so on.
$endgroup$
– Fattie
Mar 24 at 19:54
2
$begingroup$
@rcgldr thanks for the mention I added an extra paragraph to address that.
$endgroup$
– John K
Mar 24 at 20:01
1
$begingroup$
Stop signs on buoys! That would be rather funny, @Fattie!
$endgroup$
– FreeMan
Mar 25 at 12:34
$begingroup$
@FreeMan - right :)
$endgroup$
– Fattie
Mar 25 at 12:36
$begingroup$
How did large versions like the Ekranoplan turn? Looks like there's a fairly large rudder, and engine thrust might have been used. There doesn't seem to be much margin for bank angle.
$endgroup$
– rcgldr
Mar 24 at 18:44
$begingroup$
How did large versions like the Ekranoplan turn? Looks like there's a fairly large rudder, and engine thrust might have been used. There doesn't seem to be much margin for bank angle.
$endgroup$
– rcgldr
Mar 24 at 18:44
$begingroup$
It never occurred to me that such craft would indeed "meet" - just like ground vehicles! You'd need stop signs and so on.
$endgroup$
– Fattie
Mar 24 at 19:54
$begingroup$
It never occurred to me that such craft would indeed "meet" - just like ground vehicles! You'd need stop signs and so on.
$endgroup$
– Fattie
Mar 24 at 19:54
2
2
$begingroup$
@rcgldr thanks for the mention I added an extra paragraph to address that.
$endgroup$
– John K
Mar 24 at 20:01
$begingroup$
@rcgldr thanks for the mention I added an extra paragraph to address that.
$endgroup$
– John K
Mar 24 at 20:01
1
1
$begingroup$
Stop signs on buoys! That would be rather funny, @Fattie!
$endgroup$
– FreeMan
Mar 25 at 12:34
$begingroup$
Stop signs on buoys! That would be rather funny, @Fattie!
$endgroup$
– FreeMan
Mar 25 at 12:34
$begingroup$
@FreeMan - right :)
$endgroup$
– Fattie
Mar 25 at 12:36
$begingroup$
@FreeMan - right :)
$endgroup$
– Fattie
Mar 25 at 12:36
add a comment |
Thanks for contributing an answer to Aviation Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2faviation.stackexchange.com%2fquestions%2f61572%2fhow-do-ground-effect-vehicles-perform-turns%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
8
$begingroup$
"carefully" ....
$endgroup$
– Fattie
Mar 24 at 19:54
$begingroup$
Wouldn't the raised wing have less drag, because it's experiencing less ground effect, ergo producing less lift, ergo generating less induced drag?
$endgroup$
– Sean
Mar 25 at 2:51
2
$begingroup$
@Sean, no: the essence of the ground effect that you get more lift for the same drag. Or same lfit with less drag. Also, if you are in a sustained banked turn, then by definition both half-wings produce the same lift - otherwise you'd be rolling with acceleration. It follows that the surface that is less in ground effect will have more drag. (Plus there are usual effects due to ailerons position etc. - which usually contribute with the same sign).
$endgroup$
– Zeus
Mar 25 at 4:54