### Author Topic: General Hohmann Transfer  (Read 1593 times)

#### marklinick

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##### General Hohmann Transfer
« on: 06/12/2018 11:52 PM »
Question: Would a general Hohmann Transfer be of interest to anyone? Even just for educational value.

Background: I am ms-physics----not an orbital mechanic. I taught myself om, trying to learn orbits of planets and rings. Everywhere I looked, Hohmann transfers only apply to circular orbits or coaxial elliptical orbits. This is NOT true. Hohmann transfers apply to any two elliptical orbits in a plane, coaxial or not. But is this of interest? to anyone?

The book I used: Orbital Mechanics for Engineering Students (2005)--Howard Curtis.
See 6.7 Apse Line Rotation, Fig 6.17. He says, "A Hohmann transfer between them (the two orbits) is clearly impossible." Again, this is false.

If interested, I can post the method.

Mark
(New here. Let me know if this is posted in the wrong place)

#### QuantumG

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##### Re: General Hohmann Transfer
« Reply #1 on: 06/13/2018 12:06 AM »
Sure, sounds like a blast.
Human spaceflight is basically just LARPing now.

#### marklinick

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##### Re: General Hohmann Transfer
« Reply #2 on: 06/13/2018 10:59 PM »
This is what a general Hohmann transfer looks like. The first figure (Fig1.png) is a transfer between coaxial orbits. The second figure (Fig10.png) is a transfer between non-coaxial orbits. Here, the target apse line is rotated 25o relative to the initial orbit.

The transfer in fig10 is fuel efficient, but not optimal. It came within 1% (delta v) of an optimal transfer. However, these Hohmann, or tangent, transfers offer two advantages over an optimized transfer--safety and reliability. Therefore, tangent transfers and rendezvous may be preferred over optimizing since the fuel usage is almost the same. (I'm asking)

Again, I am assuming the state of the art is to optimize transfers.

#### 1

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##### Re: General Hohmann Transfer
« Reply #3 on: 06/14/2018 08:06 PM »
A tangential burn is exactly as safe and reliable as a burn in any other orientation. But all of this is moot as many (most?) launches involve an inclination change of some kind, and thus don't even have co-planarity between initial and target orbits working for them. I wouldn't worry about generalizing a special case of transfer orbit.

Also, your ΔV2 burn in figure 10 is in the wrong direction.

#### QuantumG

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##### Re: General Hohmann Transfer
« Reply #4 on: 06/15/2018 12:52 AM »
Well, it's always best to do inclination changes when you're going fastest... so I can't tell from these diagrams if what you're doing is optimal. I'd just do the first burn so the transfer ellipse has its apoapsis as the periapsis of the desired orbit, then do the plane change and any circularization when you get there.
Human spaceflight is basically just LARPing now.

#### marklinick

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##### Re: General Hohmann Transfer
« Reply #5 on: 06/15/2018 05:50 AM »
It is not moot. You want to "incline" the best orbit. Let me show this in the plane, first.

Now, I would like to give my (new) definition of a Hohmann transfer.

A Hohmann transfer is a tangent transfer, but it is not the only tangent transfer (an ellipse tangent to the initial and target orbit). Below are two tangent transfers generated numerically at opposite apse points. There is a range of these types of transfers. Observe one transfer is larger than the other, i.e. more energetic--requires higher delta v's and fuel to effect a transfer.

I claim a Hohmann transfer is the most fuel efficient tangent transfer between any two orbits in a plane.

I wish to clear up a point of confusion. Notice I did not use the word "optimal" in my definition. Optimization is the method used since the 1960's for orbital transfers (to the best of my knowledge). The procedure numerically minimizes (optimizes) a variable of interest (delta v's) from a set of orbital equations--think LaGrange multipliers. It produces the most fuel efficient transfer ellipse between two orbits--no gas stations in space.

I am not optimizing anything. Still, a Hohmann transfer is fuel efficient by nature. It is not optimal in fuel, but very close. It should be considered for transfers and rendezvous. Why? It is safer and more reliable than an optimized transfer, as I will show in a bit.

#### meberbs

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##### Re: General Hohmann Transfer
« Reply #6 on: 06/15/2018 05:31 PM »
First, a note: When you are new to a subject, read specialized textbooks on that subject, and then declare that the statements in the textbook "are NOT true," you need to take a step back and ask what it is that you don't know about this field.

However, these Hohmann, or tangent,
Hohmann is not a synonym for tangent. It is defined as the most energy efficient transfer between 2 co-planar circular orbits. The reason for the restrictions on the applicability of Hohmann transfers in the textbooks is because they are there by definition. For a generalized Hohmann transfer definition it would be better to use either "most efficient 2 burn transfer" or "most efficient transfer" between 2 arbitrary elliptical orbits. (second definition allows options like a 3rd burn mid way to adjust inclination, which can be useful.)

Again, I am assuming the state of the art is to optimize transfers.
I wish to clear up a point of confusion. Notice I did not use the word "optimal" in my definition. Optimization is the method used since the 1960's for orbital transfers (to the best of my knowledge). The procedure numerically minimizes (optimizes) a variable of interest (delta v's) from a set of orbital equations--think LaGrange multipliers. It produces the most fuel efficient transfer ellipse between two orbits--no gas stations in space.
"Optimal" means best under the relevant metric (which can be an aggregation of lower level metrics). Optimization does not have to be done numerically. It is often done numerically for orbits, because there aren't nice closed form solutions.

As for the "state of the art" Hohmann transfers are good first approximations of delta-v requirements for many missions. For things like interplanetary missions, the state of the art provides performing full multi-body gravity simulations (for which it is known that there is no closed form solution.) These are searched to also include special trajectories with flybys. Tradeoffs and windows are established so launches can be done outside the exact day specified by a Hohmann transfer, and extra fuel used to reduce the trip time.

One major problem you are ignoring is that for many cases (particularly interplanetary) you need the timing to line up so the planet is there when you get there. Your "tangential" transfers don't account for that.

Well, it's always best to do inclination changes when you're going fastest... so I can't tell from these diagrams if what you're doing is optimal. I'd just do the first burn so the transfer ellipse has its apoapsis as the periapsis of the desired orbit, then do the plane change and any circularization when you get there.
I think you got something backwards. Inclination changes you want to be going slow for. The diagrams are not showing inclination changes, marklinick is still discussing co-planar examples. It is burns such as apoapsis raising (similar to what the diagrams show) where you are getting benefits from the Oberth effect.

#### 1

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##### Re: General Hohmann Transfer
« Reply #7 on: 06/15/2018 10:04 PM »
It is not moot. You want to "incline" the best orbit. Let me show this in the plane, first.

...No.

Inclination is a property of an orbit, not something that you do to it. You can think of it as a tilt relative to another fixed plane of reference (for Earth based launches, the equator). This is elementary.

Now, I would like to give my (new) definition of a Hohmann transfer.

Again, no. If you're going to argue that a textbook is incorrect, then you need to use the definitions as given in the textbook; not your own personal preference. The definition as given in section 6.3 of that book is this:

Quote
The Hohmann transfer (Hohmann, 1925) is the most energy efficient two-impulse maneuver for transferring between two coplanar circular orbits sharing a common focus.

“Orbital Manuvers.” Orbital Mechanics for Engineering Students, by Howard D. Curtis, Elsevier, 2014.

Note the "Hohmann, 1925" citation; indicating that this is very likely how the transfer was defined by Hohmann himself. This means that this book, and all others using this definition, are correct.

If you want to focus on tangential burns, great, but the book's approach (as clearly seen in example 6.7) is to change orbits using a single burn at a point where the two orbits intersect. If you want to keep our attention (as well as reduce the probability of this thread getting locked) perhaps take example 6.7 and calculate total delta-v required for a two-tangential-burn maneuver, and see how the numbers compare.

#### marklinick

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##### Re: General Hohmann Transfer
« Reply #8 on: 06/15/2018 11:17 PM »
"Not true" was meant to get attention, not to be rude. No disrespect to the author or anyone else. He taught me.

Still, let me take this opportunity to defend it, and my definition.

1) It is appropriate to classify the Hohmann transfer as a type of tangent transfer. It touches the initial and target orbits at one point.  Contrast with an optimized orbit transfer, which crosses the initial and target orbits at two points. Strange (not obvious)--given it is the most fuel efficient transfer--but true.

2) Please forgive fig8 below...it is confusing. Each dashed curve is a transfer ellipse, tangent to the initial and target orbits. They are generated at 10 degree intervals...I think. I calculate the efficiency of each so I can compare them in Fig9a.

Each transfer ellipse is rated for energy (total delta v). Fig6 above, generated at 0o, is about 2 Km/s total delta v. Fig7 above, generated at 180o, is about 1 Km/s. The most efficient tangent transfer is about 77o at about 0.71 Km/s total delta v. This is fig10 above.

3) Question: What is so special about the angles 770 and 224o (fig10 above) that allows me to call this most fuel efficient tangent transfer, a Hohmann transfer?

Answer: The initial and target orbits are tangent at these angles....and only these angles. This is the case between circular orbits, except circular orbits are tangent everywhere, i.e. a Hohmann transfers fit everywhere. Hohmann is a synonym for tangent.

#### marklinick

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##### Re: General Hohmann Transfer
« Reply #9 on: 06/16/2018 02:33 AM »
1) The definition in the book is correct for the special case of circular orbits. If you believe what I am telling you is correct, it either has to be modified or I can change the name of what I do. But what I do sure looks like a Hohmann transfer.

2) Look at fig10 above (or fig6 and fig7 above). Do they look familiar?? Those are the orbits from example 6.7!!!! Example 6.7 motivated me to find a transfer similar to the Hohmann transfer for circular orbits.

For example 6.7

--  The total delta v is 1.503 Km/s using a single burn at the node (like the book)

--  The total delta v is 0.71 Km/s using a my transfer ellipse (see fig10 above)--more than double the efficiency!

--  Look at fig9a. Fig10 is located at 77o on this graph. But there are a wide range of transfers more efficient than the procedure in the book.

#### gongora

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##### Re: General Hohmann Transfer
« Reply #10 on: 06/16/2018 03:03 AM »
or I can change the name of what I do.

That may be the best course of action.  You can't just change the definition of something that has existed for decades with a particular meaning.

#### QuantumG

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##### Re: General Hohmann Transfer
« Reply #11 on: 06/16/2018 03:28 AM »
I think you got something backwards. Inclination changes you want to be going slow for.

Really? I guess that's true from the perspective of the transfer orbit. Fair enough.

Quote from: meberbs
The diagrams are not showing inclination changes, marklinick is still discussing co-planar examples.

Then I completely misunderstood what he was talking about.

Human spaceflight is basically just LARPing now.

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