LethalDose Posted December 17, 2014 Share Posted December 17, 2014 (edited) Okay, well, since we're editing everything, taken from the OP:Nevertheless, Kerbin isn't the only planet. My question is if you are on the Mun such that Kerbin is perpetually setting (since the Mun is tidally locked) i.e. on the rear-side of the planet w.r.t. Mun's velocity vector, do you want to get into LMO first or go straight vertical to return to Kerbin.My preliminary math shows it takes less deltaV to go straight up (807 m/s) vs. hopping up to 10 km altitude (to avoid hitting terrain) and then burning horizontally until escape velocity is achieved (964 m/s). Since Mun's gravity is small, TWR will inevitably be large so gravitational losses will be small/negligible.What do you guys think?To me, this has always been about This has always been about Munar escape. Edited December 17, 2014 by LethalDose Link to comment Share on other sites More sharing options...
Fyrem Posted December 17, 2014 Share Posted December 17, 2014 Slash, you totally missed the entire discussion between arki and 5horseman.that is what the $10,000 challenge, Kerbin (with FAR) to Mun is all about... since YOU (slash) do not have FAR, Arki and 5thHorsman chose to design their own test. You (Slash) are not involved in it. Link to comment Share on other sites More sharing options...
Kesa Posted December 17, 2014 Share Posted December 17, 2014 This isn't quite right. First off, it should be g - vh^2/v0^2: minus, not times (otherwise it says gravity is zero when you aren't moving and it's g when you're at orbital speed).Secondly, when I take that as my apparent gravity and thrust horizontal plus just up enough to beat that apparent gravity, I end up rising -- which I shouldn't. So something is weird. Either a bug in the math here, or a bug in my code (likely).Well, I was only talking of the centrifuge force, which actually is g * vh^2/v0^2 (vh^2/v0^2 is dimensionless! so can't be substract to g). If you want to pair it with the gravity, then you have to substract it to the gravity and have :apparent gravity = g * (1 - vh^2/v0^2).Then you should be good with your sim .I'll update my post to make it clearer. Link to comment Share on other sites More sharing options...
GoSlash27 Posted December 17, 2014 Share Posted December 17, 2014 LD, Full stop for a second. I don't think we are all on the same subject at the moment. See my previous post. Exactly what are we discussing right now? My impression is that it's getting a lander off the surface of the Mun and back to Kerbin as efficiently as possible. LD, what are you talking about? Likewise you, Arkie. Link to comment Share on other sites More sharing options...
LethalDose Posted December 17, 2014 Share Posted December 17, 2014 (edited) LD, Have you ever launched a lander off the mun? If so, did you launch it vertically and pitch eastward like everybody else? I ask this in all seriousness because I can't fathom any other reason why any of this would puzzle you. Believe me, I'm not assuming that you're clueless. This *HAS* to be a failure in communication.Truly confused now,-SlashyYes. I've launched many landers off the mun.Some into parking orbits, launching east.Some straight up off the backside near the twin craters retrograde out of the Mun's orbit.It may surprise you that statements like this:did you launch it vertically and pitch eastward like everybody else? are complete crap.Not "everyone" does it that way because you gain practically nothing doing it that way. The Mun is tidally locked and, as I've stated, has an equatorial rotation speed of nine. meters. per. second.That is nothing.I've launched straight up off the Munar surface for escape, and in my experience, there was very little difference in dV costs compare to parking orbits. In fact it's how I prefer to launch when I'm near the twin craters because you just fire up until you get a Kerbin intercept.And I'm the one who actually provided some evidence for my position! Seriously, produce something tangible, or stop wasting our time. Edited December 17, 2014 by LethalDose Link to comment Share on other sites More sharing options...
GoSlash27 Posted December 17, 2014 Share Posted December 17, 2014 Slash, you totally missed the entire discussion between arki and 5horseman.that is what the $10,000 challenge, Kerbin (with FAR) to Mun is all about... since YOU (slash) do not have FAR, Arki and 5thHorsman chose to design their own test. You (Slash) are not involved in it.Fair enough. I don't know what *that* subject has to do with the OP in *this* thread, so please excuse my confusion. Arkie's got a bunch of different threads on this same subject (vertical escape vs horizontal) and I'm having a hard time keeping them all straight, especially when the topics don't match the subjects.Best,-Slashy Link to comment Share on other sites More sharing options...
LethalDose Posted December 17, 2014 Share Posted December 17, 2014 (edited) LD, Full stop for a second. I don't think we are all on the same subject at the moment. See my previous post. Exactly what are we discussing right now? My impression is that it's getting a lander off the surface of the Mun and back to Kerbin as efficiently as possible. LD, what are you talking about? Likewise you, Arkie.Yeah, I read it. We'reI'm talking about Munar surface to escape, same as you. We can talk about a Munar escape that intercepts Kerbin instead of a munar escape that just leaves the SOI.It ain't gonna change the facts I presented much, if at all. Edited December 17, 2014 by LethalDose Link to comment Share on other sites More sharing options...
GoSlash27 Posted December 17, 2014 Share Posted December 17, 2014 *caustic invective* LD, Please hold until Arkie responds so we can all get on the same page. I think you and I are talking about the same subject (escape from munar surface to Kerbin), but I don't think he was.Patience,-Slashy- - - Updated - - -Yeah, I read it. We'reI'm talking about Munar surface to escape, same as you. We can talk about a Munar escape that intercepts Kerbin instead of a munar escape that just leaves the SOI.It ain't gonna change the facts I presented much, if at all.Okay, good. So now let's wait until he responds so we're sure we're not getting crossed-up here. Link to comment Share on other sites More sharing options...
GoSlash27 Posted December 17, 2014 Share Posted December 17, 2014 (edited) Dammit! Arkie's offline. LD, how would you like to proceed? Do you want to discuss the subject that you and I were discussing in the meantime, or table it? We were both on the same topic (munar surface to Kerbin) Edited December 17, 2014 by GoSlash27 Link to comment Share on other sites More sharing options...
LethalDose Posted December 17, 2014 Share Posted December 17, 2014 Dammit! Arkie's offline. LD, how would you like to proceed? Do you want to discuss the subject that you and I were discussing in the meantime, or table it? We were both on the same topic (munar surface to Kerbin)I'm waiting for you to produce some evidence, any evidence counter to what I've stated.Vertical burns off the munar surface can be slightly less efficient than horizontal burns to escape back to Kerbin's space, whether they're made directly to escape altitudes or if they're stop-over in a parking orbit first. I've presented evidence supporting this.If you're just going to tell everyone how you can design a rocket that is just astoundingly better than anything for a vertical ascent, save it, It's a waste of time. I'll have something to say when you present anything to demonstrate your position. Link to comment Share on other sites More sharing options...
arkie87 Posted December 17, 2014 Author Share Posted December 17, 2014 (edited) LD, Full stop for a second. I don't think we are all on the same subject at the moment. See my previous post. Exactly what are we discussing right now? My impression is that it's getting a lander off the surface of the Mun and back to Kerbin as efficiently as possible. LD, what are you talking about? Likewise you, Arkie.When i referred to 5thHorseman's challenge (the 10k$ vehicle that you said you could do for 2k$), I am talking about this, as i have said multiple times:Many people (including myself) have made this argument already.... I dont know why you keep on bringing it up.This isnt a design question (yet... see below); it is a hypothetical question of what to do if you find yourself in X scenario. I actually think the case 5thHorseman suggested is a perfect test of this:We have a lander craft that must be lifted to orbit around the Mun. This craft is specified it cannot be changed. The challenge is to design the lifter stage(s). He has 5 SRB's in two stages (3 first, then 2) and will launch horizontally from Kerbin into LKO followed by periaps transfer to Mun; I will have 5 SRB's as well, but in one stage burning vertically. We will both be using the same craft, but with different staging. Same potential TWR, same mass, same cost, same everything just the optimal staging for each burn. This design by 5thHorseman is the result of trying to minimize cost (<10k$). And we see, that by minimizing cost, we are led to a design with SRB's that has a potentially high TWR. Furthermore, we can manipulate this design (without adding or removing parts--just staging) to have a high TWR-- optimal for vertical ascent-- or low TWR--optimal for horizontal.I think you really need to read what I wrote rather than responding so quickly. The challenge is to take a lander from kerbins surface and get it into orbit around mun. If you can do that for 2000 kerbucks, then I and 5thhorseman will be shocked.You really need to read what I wrote. Lander from surface of kerbin to orbit around mun. Not surface of mun to kerbin. I honestly can't tell if you are just a troll...I am not confused by my different cases/questions/scenerios/threads. If you would read what i wrote, thought about it, made sure you understood it, instead of replying so fast assuming i was saying something wrong/saying something other than i was saying...Admittedly, it's partially my fault for entertaining the Kerbin-to-Mun debate in the wrong thread. I would create a new thread, but then I would get yelled at for creating too many new threads...Perhaps 5thHorseman wants to create a new thread with his/our challenge? I would happily do it if people dont wouldnt get annoyed at me for starting too many threads about "seemingly" the same topic... clearly, they arent the same topic... Edited December 17, 2014 by arkie87 Link to comment Share on other sites More sharing options...
LethalDose Posted December 17, 2014 Share Posted December 17, 2014 Uh, yeah, Arkie... You gotta try to understand the what you said in that last quote (with the "just a troll" line) is kinda contra to what you have in your original post.Probably where a lot of the confusion is coming from. Link to comment Share on other sites More sharing options...
Kesa Posted December 17, 2014 Share Posted December 17, 2014 (edited) Great work. It should worth it to make it for escape with desired velocity.But, if you are just to leave the SOI of a planet, what is the "direct elliptical ascent"?The ellipse with AP just passing SOI that has the less energy (therefore the less velocity at see level) actually is the degenerated one obtained by verticle launch. Also, does the parking cost include gravity loss?edit : Does direct "elliptical ascent" dv requirement takes into account TWR and gravity loss? (cause it would make sense for me) Edited December 17, 2014 by Kesa Link to comment Share on other sites More sharing options...
GoSlash27 Posted December 17, 2014 Share Posted December 17, 2014 arkie, Welcome back. Okay, cool... that whole "5th Horseman" thing is between you two and since it requires FAR, I'll happily butt out. But in my defense, 1) You were the one who mentioned somewhere (forget which thread) citing your earlier statements rather than telling someone else to find them and 2) the phrase " We have a lander craft that must be lifted to orbit around the Mun." is sufficiently vague as to make someone *think* that you were referring to the munar surface, given the topic of this thread. I'm trying to follow you here as best I can, so please bear with me. Regards, Slashy Link to comment Share on other sites More sharing options...
arkie87 Posted December 17, 2014 Author Share Posted December 17, 2014 (edited) arkie, Welcome back. Okay, cool... that whole "5th Horseman" thing is between you two and since it requires FAR, I'll happily butt out. But in my defense, 1) You were the one who mentioned somewhere (forget which thread) citing your earlier statements rather than telling someone else to find them and 2) the phrase " We have a lander craft that must be lifted to orbit around the Mun." is sufficiently vague as to make someone *think* that you were referring to the munar surface, given the topic of this thread. I'm trying to follow you here as best I can, so please bear with me. Regards, SlashyI understand. I take partial responsibility, but I DID repeat for you the problem statement (nearly in full): I actually think the case 5thHorseman suggested is a perfect test of this:We have a lander craft that must be lifted to orbit around the Mun. This craft is specified it cannot be changed. The challenge is to design the lifter stage(s). He has 5 SRB's in two stages (3 first, then 2) and will launch horizontally from Kerbin into LKO followed by periaps transfer to Mun; I will have 5 SRB's as well, but in one stage burning vertically. We will both be using the same craft, but with different staging. Same potential TWR, same mass, same cost, same everything just the optimal staging for each burn. This design by 5thHorseman is the result of trying to minimize cost (<10k$). And we see, that by minimizing cost, we are led to a design with SRB's that has a potentially high TWR. Furthermore, we can manipulate this design (without adding or removing parts--just staging) to have a high TWR-- optimal for vertical ascent-- or low TWR--optimal for horizontal. And in my defense, this case is a perfect motivation behind the TWR debate (which is present in this thread as well), since optimizing for cost leads you to use SRB's (in FAR), and optimal SRB usage leads to staging for horizontal ascent, and high TWR for vertical ascent without having to change the craft design. It is therefore not an unrelated topic/case by any means....Should i make a new thread to discuss the 5thHorseman challenge? Edited December 17, 2014 by arkie87 Link to comment Share on other sites More sharing options...
GoSlash27 Posted December 17, 2014 Share Posted December 17, 2014 I'm waiting for you to produce some evidence, any evidence counter to what I've stated.Vertical burns off the munar surface can be slightly less efficient than horizontal burns to escape back to Kerbin's space, whether they're made directly to escape altitudes or if they're stop-over in a parking orbit first. I've presented evidence supporting this.If you're just going to tell everyone how you can design a rocket that is just astoundingly better than anything for a vertical ascent, save it, It's a waste of time. I'll have something to say when you present anything to demonstrate your position.LD, I will happily go through this with you, but if we are to do that, you *must* drop the attitude and conduct yourself in a civil manner. If you can't/won't do that, then I'd just as soon spend my time doing other things. Now with that said, I was not asking you "have you ever launched eastward from the munar surface" trying to be snarky, I wanted to confirm that we had a common basis for understanding, so that we both understand that leaving the surface vertically, then rotating Eastward is *not* a mutually exclusive concept. You have done it yourself, so when I say "leave the surface vertically and depart east", we should not have any confusion about what that means. You attacked me for saying that, as if I can't do both. Now clearly, *you* were referring to something else entirely when you read that, and I'm not sure what it is, but I *suspect* that you were referring to some scenario where you leave the surface heading eastbound and assumed a constant pitch. Now... I promise to be civil and respectful and I ask that you do the same. If you're cool with that, then we can proceed.Best,-Slashy Link to comment Share on other sites More sharing options...
arkie87 Posted December 17, 2014 Author Share Posted December 17, 2014 Uh, yeah, Arkie... You gotta try to understand the what you said in that last quote (with the "just a troll" line) is kinda contra to what you have in your original post.Probably where a lot of the confusion is coming from.I understand. But I made it clear i was talking about the case with 5thHorseman. And i repeated the important parts of the problem statement, and for the reasons i gave above, it was relevant to this discussion since it motivates/gives a good practical case where you might have high TWR (since SRB's are so cheap). Link to comment Share on other sites More sharing options...
LethalDose Posted December 17, 2014 Share Posted December 17, 2014 Great work. It should worth it to make it for escape with desired velocity.But, if you are just to leave the SOI of a planet, what is the "direct elliptical ascent"?The ellipse with AP just passing SOI that has the less energy (therefore the less velocity at see level) actually is the degenerated one obtained by verticle launch. Also, does the parking cost include gravity loss?Sorry, man. I'm having a lot of difficulty following what you're asking or saying.The "direct elliptical ascent" is intended to be "lower bound" for the cheapest burn from the surface to escape. It's essentially the dV cost of an an instantaneous impulse that accelerates the vessel to "escape velocity" (though technically, it's the velocity to reach the SOI. I was trying to compare similar values). I called it "direct elliptical ascent" to differentiate it from the The parking orbit calculations don't include gravity losses, but they aren't really needed. It's a combination of 3 burns: a surface to parking orbit transfer (similar to what I just described, but to an AP of 10 km, instead of the SOI border)circularization burn at APa parking-to-SOI border burnThe only place gravity losses would really need to be accounted for are during the burns. Otherwise, gravity losses are kind of "included" in the calculations, since we know we're going slower up at the APs than the PEs.The goal, really, was just to describe an escape. I was not aiming for some specific velocity at escape (other than >0). However which would be of interest if you were trying to change orbit, e.g. drop down to Kerbin's atmosphere.Even though I think I see what you're saying in the final part, I don't like thinking of the vertical climb as a degenerate case, because the rocket is burning over a wide range of altitudes, which changes how it is inputting energy into the system. In the other examples, The prograde burns are made at roughly the same altitudes, which makes the assumption of an 'instant impulse' much more palatable, at least to me. Link to comment Share on other sites More sharing options...
GoSlash27 Posted December 17, 2014 Share Posted December 17, 2014 I understand. I take partial responsibility, but I DID repeat for you the problem statement (nearly in full): *quote* Aye, and I read it in full, but if you read it, you will see that there's absolutely nothing in there that would lead a reader to conclude that you were talking about departing from Kerbin instead of the mun.Easy mistake to make, given the circumstances.Best,-Slashy Link to comment Share on other sites More sharing options...
arkie87 Posted December 17, 2014 Author Share Posted December 17, 2014 Aye, and I read it in full, but if you read it, you will see that there's absolutely nothing in there that would lead a reader to conclude that you were talking about departing from Kerbin instead of the mun.Easy mistake to make, given the circumstances.Best,-SlashyIn my description of the orbit, i said departing from kerbin, but the original description was vague. However, i clarified it twice thereafter. Link to comment Share on other sites More sharing options...
LethalDose Posted December 17, 2014 Share Posted December 17, 2014 (edited) LD, I will happily go through this with you, but if we are to do that, you *must* drop the attitude and conduct yourself in a civil manner. If you can't/won't do that, then I'd just as soon spend my time doing other things. Now with that said, I was not asking you "have you ever launched eastward from the munar surface" trying to be snarky, I wanted to confirm that we had a common basis for understanding, so that we both understand that leaving the surface vertically, then rotating Eastward is *not* a mutually exclusive concept. You have done it yourself, so when I say "leave the surface vertically and depart east", we should not have any confusion about what that means. You attacked me for saying that, as if I can't do both. Now clearly, *you* were referring to something else entirely when you read that, and I'm not sure what it is, but I *suspect* that you were referring to some scenario where you leave the surface heading eastbound and assumed a constant pitch. Now... I promise to be civil and respectful and I ask that you do the same. If you're cool with that, then we can proceed.Best,-SlashyI've made it very clear what I'm talking about: leaving the surface vertically, and then continuing to burn vertically.I've asked very clearly for examples of your boastful claims in your multiple and exceptionally rude posts, including, but not limited to:But that's a crap design and nobody's going to find themselves in that scenario! That's *my* point. It goes back to "crappy rocket is crappy no matter which way you point it". Why would anyone in their right mind design a $10,000 heap with 5 (five!!) SRBs when they can do the job for less than $2,000, 1.4T total mass, and a half ton of liquid fuel?? And that's without really trying. And what monstrosity are you gonna use just to place that Edsel on the Munar surface? You gotta do the TMI hauling that ginormous payload, and get all of that off of Kerbin. And you think the differences between these two approaches will be "marginal"?? I'm half- tempted to expand the challenge to a full Munar mission from launch to splashdown and spot you the 1Km/sec+ advantage from running FAR, it's so bad. What started this whole ballyhoo was the idea that "maybe vertical launch isn't as awful as people think", but as a practical matter, it *is* awful. Not just awful, but truly *horrendous*.Sorry,-SlashyAndI understand all that, but he's wasting his time. You are not constrained to maintain a single pitch angle during a launch, and your t/w increases as fuel burns off, so launching at 1G vertically means that you *will* rise from the moment the first molecule of fuel meets the first molecule of oxygen. You don't need a huge t/w to get off the mun in an eastbound trajectory, and everyone who's ever played KSP already knows this.Scratchin' mah head,-SlashyAndFAR and stock are identical out of atmosphere, so we can directly compare results. I can build a rocket that will outperform your best vertical effort in every category of efficiency in the scenario you have proposed here. DV, cost, fuel consumption, total vehicle mass... everything. And the difference between these two vehicles wouldn't be anything you could call "minor".. The scenario is as follows: Place a vehicle of your own design (stock parts, no cheats) in the location you describe carrying a Mk.1 command pod as payload. Build it to be as efficient as you can and post the specs (mass, cost, fuel). Then escape from the Mun vertically and establish a periapsis within Kerbin's atmosphere. Again, post mass and fuel state. You may use solar panels to provide power, since they are massless. You may deduct the cost of the solar panels for the purposes of this exercise. You will not be charged for any parts you use to place the lander on the surface itself or decouplers to detach the launch vehicle from the lander, as placing the payload on the surface is not part of the test. I will do the same, but going horizontal. I guarantee my rocket will blow your rocket's doors off.Best,-SlashyFinally, you're not a moderator. You have no place to criticize my behavior. You are in position to comment let alone dictate how I must behave or what kind of attitude I'm allowed to have. Especially given your recent behavior in this thread and multiple other threads.Take you're condescension and shove it. You've proved repeatedly you can't, or won't, be "civil and respectful". You're nothing more than an empty braggart who can't be communicated with. Edited December 17, 2014 by LethalDose Link to comment Share on other sites More sharing options...
GoSlash27 Posted December 17, 2014 Share Posted December 17, 2014 In my description of the orbit, i said departing from kerbin, but the original description was vague. However, i clarified it twice thereafter.Yes you did. *After* you had already concluded I was trolling you and berating me for it, not before. At the time, I was operating under the assumption that you were referring to a departure from the Mun, which is not unreasonable given the vague nature of the post and the topic of this thread. Not belaboring the point, just making absolutely sure that you understand: I've got better things to do with my time than troll you. If you're under the impression that I'm doing that, then it's due to some confusion in our communication, *not* an intentional effort on my part. Best,-Slashy Link to comment Share on other sites More sharing options...
arkie87 Posted December 17, 2014 Author Share Posted December 17, 2014 Yes you did. *After* you had already concluded I was trolling you and berating me for it, not before. At the time, I was operating under the assumption that you were referring to a departure from the Mun, which is not unreasonable given the vague nature of the post and the topic of this thread. Not belaboring the point, just making absolutely sure that you understand: I've got better things to do with my time than troll you. If you're under the impression that I'm doing that, then it's due to some confusion in our communication, *not* an intentional effort on my part. Best,-SlashyTo be honest, when we have miscommunications that last for days, i start to wonder if you are trolling me. But then when we resolve them, i see your point of view and what you thought, and realize you werent trolling, but rather, had a legitimate point or misunderstanding.But when this happens again and again, i start to wonder. To clarify, i didnt mean to call you a troll (i was saying i was starting to wonder), and i dont think you are a troll. It was all jut a misunderstanding. Link to comment Share on other sites More sharing options...
GoSlash27 Posted December 17, 2014 Share Posted December 17, 2014 (edited) LD, flamebait Fair enough. You and I simply won't converse. I think that's best for all the users on this forum. But a Munar ascent vehicle that falls within the limits I outlined isn't "boastful", it's common practice. Not even optimized. If you slap together a Mk 1 command pod, an FL-T100 tank, and an LV-1 engine, it's completely adequate to get you back to Kerbin from the Munar surface with plenty of DV to spare. Not like that's any huge engineering miracle. There's no high- acceleration monster that's ever going to beat that in a vertical departure when it's departing east for any measure of efficiency. It's lighter, cheaper, burns less gas, and expends less DV. A *lot* less in all categories. Sorry we couldn't get on the same page,-Slashy- - - Updated - - -To be honest, when we have miscommunications that last for days, i start to wonder if you are trolling me. But then when we resolve them, i see your point of view and what you thought, and realize you werent trolling, but rather, had a legitimate point or misunderstanding.But when this happens again and again, i start to wonder. To clarify, i didnt mean to call you a troll (i was saying i was starting to wonder), and i dont think you are a troll. It was all jut a misunderstanding.Agreed, and no hard feelings. All it *really* means is that we miscommunicate frequently I will leave you and 5thHorseman to sort out your challenge. When you want to discuss vertical vs. horizontal munar departure, I'll pick it up there. Best,-Slashy Edited December 17, 2014 by GoSlash27 Link to comment Share on other sites More sharing options...
arkie87 Posted December 17, 2014 Author Share Posted December 17, 2014 - - - Updated - - -Agreed, and no hard feelings. All it *really* means is that we miscommunicate frequently I will leave you and 5thHorseman to sort out your challenge. When you want to discuss vertical vs. horizontal munar departure, I'll pick it up there. Best,-SlashyYes, let's resume to discussing munar vertical vs horizonal.We do seem to mis-communicate frequently.... LD, But a Munar ascent vehicle that falls within the limits I outlined isn't "boastful", it's common practice. Not even optimized. If you slap together a Mk 1 command pod, an FL-T100 tank, and an LV-1 engine, it's completely adequate to get you back to Kerbin from the Munar surface with plenty of DV to spare. Not like that's any huge engineering miracle. There's no high- acceleration monster that's ever going to beat that in a vertical departure when it's departing east for any measure of efficiency. It's lighter, cheaper, burns less gas, and expends less DV. A *lot* less in all categories. Sorry we couldn't get on the same page,-SlashyLethalDose wasn't saying that a launch vehicle under 10k$ (at 2k$) is ridiculous. That was me and 5thHorseman since we were talking about his challenge, and not the one outlined by this thread's OP. You might want to go back and reread (i can imagine if everyone is yelling at you, it's hard to remember who is who )LethalDose was just asking you to quantify what you were saying with equations, math, or in-flight tests, rather than words (since otherwise, you just repeat yourself). Link to comment Share on other sites More sharing options...
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